Weyl multiplets of N=2 conformal supergravity in five Dimensions

Antoine Van Proeyen; Eric Bergshoeff; Martijn Derix; Rein Halbersma; Sorin Cucu; Tim de Wit

REVIEW

Weyl multiplets of N=2 conformal supergravity in five Dimensions

Eric Bergshoeff, Sorin Cucu, Martijn Derix, Tim de Wit, Rein Halbersma, Antoine Van Proeyen

High Energy Physics - Theory · Submitted 12 Apr 2001 · 41 references

Pith's verdict: A careful, self-contained construction of the 5D Weyl multiplets; the real soft spot is the asserted match with (3.14), not the dualization in 5.3.

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arXiv IDhep-th/0104113 (version 4)

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CitationAntoine Van Proeyen, Eric Bergshoeff, Martijn Derix, Rein Halbersma, Sorin Cucu, Tim de Wit. "Weyl multiplets of N=2 conformal supergravity in five Dimensions." arXiv:hep-th/0104113 (2001). https://pith.science/paper/Q5KTEBTZ

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Editor's note

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This is the paper that fills in the D=5 entry of the superconformal tensor-calculus program, and it does so cleanly. Two Weyl multiplets, Standard and Dilaton, same gauge fields, different matter content, both 32+32, plus the full soft algebra in (4.3)-(4.7). The Dilaton multiplet is genuinely new; the Standard one overlaps with Nishimura [5], which the authors say plainly, and the Note Added discloses Fujita-Ohashi [41] appearing days later. That is honest bookkeeping, not a hidden priority grab. The construction itself is the standard one done properly: gauge F^2(4), impose the conventional constraints (3.9), solve for omega, phi, f in (3.11), add matter, and check closure with field-dependent parameters. Sections 3 and 4 are the meat and they read as competent algebra, not hand-waving. Section 2's current-multiplet route is also worth having: the observation that the D=5 vector energy-momentum tensor is neither traceless nor improvable, and that a dilaton in the Weyl multiplet is what rescues the coupling, is a nice piece of physics reasoning that explains why two versions exist at all. On the stress-test note: it is right and the reader is wrong about section 5.3. Rewriting H_a=0 as a Bianchi identity for a dual two-form is a standard 5D identity, guaranteed by the definition (5.17), not an extra assumption. The genuinely load-bearing sentence is the one after it, 'The expressions for these fields exactly coincide with the ones we found in (3.14).' That coincidence is the whole content of the abstract's claim that the Dilaton multiplet follows from solving the improved-vector EOM, and it is asserted rather than shown term by term. I would want the chi, D, T_ab coefficients checked explicitly. Second, the soft algebra (4.3)-(4.7) with its field-dependent K-parameter is presented without a Jacobi check; closure is what makes 'full non-linear' mean something. Both are fixable in revision, neither sinks the paper. The authors already flag the unanalyzed non-local counterterms and the unsubstituted D in (3.14). Who should read it: anyone building matter couplings in 5D, and the AdS6/CFT5 and domain-wall crowd. It deserves referees, mainly to force the (3.14) match into print.

Referee report

Significance

If correct, this is the first complete construction of five-dimensional N=2 conformal supergravity and supplies the tensor-calculus ingredients (transformation rules, covariant curvatures, Bianchi identities, and the modified soft algebra) needed for general matter couplings in D=5, which the authors identify as the motivation. The paper is explicit and checkable: the constraints, their solutions, the curvatures, and the full commutator algebra are all written out, so the algebraic claims can be verified independently. The dualization argument of section 5.3 relating the two multiplets is a clean structural result, and the reducibility analysis of the Howe-Lindstrom multiplet in Appendix C is a useful byproduct that clarifies the older literature. The construction is also a natural bridge to the AdS6/CFT5 discussion and to the F(4)-gauged six-dimensional theory, which the authors flag as a direction.

Major objections (2)

[Section 5.3] The sentence 'The expressions for these fields exactly coincide with the ones we found in (3.14)' is the crux of the claim in abstract:s4 that the Dilaton multiplet is obtained by solving the equations of motion, but the coincidence is asserted rather than demonstrated. The paper does display both sides, (3.14) and (5.12)-(5.14), so the comparison is in principle checkable, but the reader is left to verify the matching of chi^i, D, and T_ab term by term, including the fermion bilinears and the T^2 and sigma^{-2} structures. This is made harder by the fact that the expression for D in (3.14) is deliberately left partly unsubstituted ('for reasons of brevity'), so the corresponding terms in (5.14) cannot be compared directly. I would ask the authors to add an explicit term-by-term comparison, or at minimum to state which structures were checked and how the cubic fermion and T^2 terms arise from the equations of motion. This is a request for added verification, not an assertion that the result is wrong.
[Section 4.3, Eqs. (4.3)-(4.7)] The modified soft algebra is presented with field-dependent parameters, including the T-dependent Lorentz rotation lambda^{ab}_3, the SU(2) parameter lambda^{ij}_3 proportional to gamma·T, and the special-conformal parameter Lambda^a_{K3} in (4.4) containing the T^2 and D T terms. Since the abstract claims 'full non-linear transformation rules', closure of this algebra is what validates the claim, and the paper does not state whether the Jacobi identities for the field-dependent structure functions have been checked. A sentence confirming that the Jacobi identities close, or noting which commutators were used to verify them, would substantially strengthen the central claim. As with the previous comment, this is a request for an explicit statement rather than an allegation of inconsistency.

Minor objections (8)

[Eq. (2.9)] The symbol rho appearing in the first term of delta_Q zeta^i = (1/2) rho epsilon^i - ... is not defined anywhere in the text or in Appendix A; presumably it is a field of the current multiplet that should be identified, and the definition should be supplied.
[Section 2.1] The statement that for the D=5 vector multiplet 'there do not exist gauge-invariant local improvement terms' is asserted without argument; a brief justification, or a pointer to where this is shown, would help the reader understand why the dilaton route is forced.
[Section 2.4] The claim that 'In 5 dimensions the full superconformal algebra cannot be realized on a matter multiplet without improvement by a dilaton' is stronger than what is demonstrated in the paper; it should either be given a short argument or softened to a statement about the multiplets considered here.
[Section 3.2] The word 'fuenfbein' appears with a broken umlaut; this should be corrected to 'fuenfbein' or replaced by 'vielbein'.
[References] Reference [40] (Behrndt and Cvetic) appears in the bibliography but does not seem to be cited anywhere in the text; either a citation should be added or the entry removed.
[Eq. (4.1)] The term '+2 Lambda_{K mu}' in the transformation of b_mu should be written explicitly as 2 Lambda^a_K e_{mu a} to match the notation of (3.2) and to make the index structure and weight counting transparent.
[Table 3 caption] The caption explains that the '#' column counts off-shell degrees of freedom with gauge degrees of freedom subtracted, but for A_mu and B_{mu nu} the counting (4 and 6) is the naive component count before gauge fixing; a clarifying phrase would prevent confusion when the reader checks the 32+32 total.
[Appendix C] The statement that the 8+8 current multiplet (C.5) is 'conjugate to the off-shell vector multiplet (5.2)' would benefit from one sentence spelling out the correspondence between the component fields, since the counting alone does not make the conjugation manifest.

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The paper

The paper claims

Five-dimensional conformal supergravity exists in two versions, and the authors construct both.

The reading

This paper constructs the Weyl multiplet of $N=2$ conformal supergravity in five dimensions, the object that a superconformal tensor calculus needs before any general matter coupling can be written down. Conformal supergravity gauges local scale, special conformal and special supersymmetry transformations on top of the usual ones; coupling its Weyl multiplet to matter multiplets is the standard route to the most general Poincaré supergravities, and the five-dimensional case had been missing. The authors gauge the exceptional superalgebra $F^2(4)$, impose conventional curvature constraints that make the spin connection, the special-conformal gauge field and the special-supersymmetry gauge field composite, and then find that the resulting $32+32$ multiplet is not unique. Two versions exist with identical gauge fields but different matter content: a Standard Weyl multiplet carrying an antisymmetric tensor $T_{ab}$, a spinor $chi^i$ and a scalar $D$, and a Dilaton Weyl multiplet carrying a vector $A_mu$, a two-form $B_{mu nu}$, a spinor $psi^i$ and a compensating scalar $sigma$ of zero mass dimension. The paper closes the loop by showing that the Dilaton version follows from coupling the Standard version to an improved vector multiplet and solving that multiplet's equations of motion.

What carries the argument

Three pieces of machinery carry the argument. The first is the gauging of $F^2(4)$ with conventional curvature constraints, which converts $P$-gauge transformations into general coordinate transformations, solves for the dependent fields $omega_mu{}^{ab}$, $f_mu{}^a$ and $phi_mu{}^i$, and reduces the gauge fields to an irreducible set. The second is the current multiplet of the on-shell vector multiplet, a $32+32$ set of currents including the energy-momentum tensor, the supercurrent, an $SU(2)$ current, and the trace parts $theta^mu{}_mu$ and $gamma cdot J$ that would normally be improved away; the dilaton makes those trace parts physical rather than obstructions, and the coupling $int (frac{1}{2} h_{mu nu}theta^{mu nu} + dots + phi, theta^mu{}_mu)$ defines the linearized Dilaton multiplet. The third is the rewriting of the vector multiplet's equation of motion $H_a = 0$ as a Bianchi identity $D_{[a}hat H_{bcd]} = frac{3}{4}hat F_{[ab}hat F_{cd]}$ with $-frac{1}{6}varepsilon_{abcde}hat H^{edc} = 8sigma^2 T_{ab} - sigma hat F_{ab} - frac{i}{4}barpsi gamma_{ab}psi$, which is what allows the antisymmetric tensor of the Standard multiplet to be traded for a two-form gauge field and thereby produces the Dilaton multiplet.

Extended reading notes

Core claim

The central claim is that five-dimensional $N=2$ conformal supergravity admits two distinct Weyl multiplets, each with $32$ bosonic and $32$ fermionic components, sharing the same gauge fields of $F^2(4)$ but differing in the matter fields that complete them. The Dilaton multiplet is derived first, at the linearized level, by the current-multiplet method: the authors compute the full $32+32$ current multiplet of the on-shell five-dimensional vector multiplet, note that its energy-momentum tensor is neither traceless nor improvable by local gauge-invariant terms, and observe that a dilaton in the gravity multiplet can absorb the trace. Coupling each current to a field then yields the linearized transformation rules. The full non-linear rules for both multiplets come from gauging $F^2(4)$ with the conventional constraints $R_{mu nu}{}^a(P)=0$, $e^{nu b}hat R_{mu nu}{}^{ab}(M)=0$ and $gamma^mu hat R_{mu nu}{}^i(Q)=0$, which leave $21$ bosonic and $24$ fermionic independent gauge components to be completed by matter. Finally, the authors show that the two multiplets are related by an explicit non-linear field redefinition: $T_{ab}$, $chi^i$ and $D$ of the Standard multiplet are expressed in terms of the Dilaton multiplet's $sigma$, $A_mu$, $B_{mu nu}$ and $psi^i$.

Load-bearing premise

The bridge between the two multiplets depends on reading the vector multiplet's equation of motion $H_a=0$ as the Bianchi identity of a two-form gauge field, which requires the specific combination $8sigma^2 T_{ab} - sigma F_{ab} - frac{i}{4}barpsi gamma_{ab}psi$ to be expressible as the curl of a three-form.

Editorial extensions

If this is right

A superconformal tensor calculus for $N=2$, $D=5$ becomes available: matter multiplets can be coupled to either Weyl multiplet and the resulting Poincaré supergravities read off, giving an independent route to the general five-dimensional matter couplings previously obtained by other means.
The two-multiplet structure found in six dimensions for $(1,0)$ conformal supergravity is confirmed to recur in five dimensions, with the antisymmetric tensor $T_{ab}$ of the Standard multiplet dual to the vector and two-form of the Dilaton multiplet.
The modified (soft) supersymmetry algebra is given explicitly, with field-dependent parameters including a $T$-dependent Lorentz rotation, a $T$-dependent $SU(2)$ rotation, and in the Dilaton version an extra $U(1)$ and vector gauge transformation; any matter multiplet coupled to these Weyl multiplets must close on this algebra.
The $40+40$ supercurrent multiplet of Howe and Lindström is shown to be reducible, splitting into the $32+32$ current multiplet used here plus an $8+8$ multiplet whose currents match an off-shell vector multiplet.
Because the Standard Weyl multiplet has no zero-mass-dimension scalar, it cannot serve as a compensating multiplet for scale invariance; only the Dilaton version can, which explains why the current-multiplet construction lands on the Dilaton version directly.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the two multiplets are genuinely equivalent on the fields they share, then the choice between them is a choice of gauge fixing rather than of theory, which would let calculations switch representations mid-stream, for instance using the two-form $B_{mu nu}$ when a dualized field strength is convenient and $T_{ab}$ when it is not.
The paper's own note that non-local improvement terms were not analysed leaves open whether the Standard multiplet can be reached from a current multiplet directly; a non-local improvement of the vector current multiplet would be the natural place to look, by analogy with the ten-dimensional case the authors cite.
The parallel drawn with four dimensions in the concluding table suggests a Dilaton multiplet in $D=4$ containing two vectors; checking whether the same equation-of-motion-to-Bianchi-identity trick works there would test whether this mechanism is dimensional or accidental.
The soft algebra's field-dependent parameters, in particular the $T$-dependent Lorentz and $SU(2)$ rotations, constrain what a consistent matter multiplet can look like; a matter multiplet whose supersymmetry variation fails to reproduce those parameters would be ruled out without any further calculation.

Original abstract

We construct the Weyl multiplets of N=2 conformal supergravity in five dimensions. We show that there exist two different versions of the Weyl multiplet, which contain the same gauge fields but differ in the matter field content: the Standard Weyl multiplet and the Dilaton Weyl multiplet. At the linearized level we obtain the transformation rules for the Dilaton Weyl multiplet by coupling it to the multiplet of currents corresponding to an on-shell vector multiplet. We construct the full non-linear transformation rules for both multiplets by gauging the D=5 superconformal algebra F^2(4). We show that the Dilaton Weyl multiplet can also be obtained by solving the equations of motion for an improved vector multiplet coupled to the Standard Weyl multiplet.

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arXiv listing abstract v4. Results and the main claim are underlined; show every role.

We construct the Weyl multiplets of N=2 conformal supergravity in five dimensions. We show that there exist two different versions of the Weyl multiplet, which contain the same gauge fields but differ in the matter field content: the Standard Weyl multiplet and the Dilaton Weyl multiplet. At the linearized level we obtain the transformation rules for the Dilaton Weyl multiplet by coupling it to the multiplet of currents corresponding to an on-shell vector multiplet. We construct the full non-linear transformation rules for both multiplets by gauging the D=5 superconformal algebra F^2(4). We show that the Dilaton Weyl multiplet can also be obtained by solving the equations of motion for an improved vector multiplet coupled to the Standard Weyl multiplet.

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s0	We construct the Weyl multiplets of N=2 conformal supergravity in five dimensions.	contribution 1.00	0.96	0.40	asserted 1.00
s1	We show that there exist two different versions of the Weyl multiplet, which contain the same gauge fields but differ in the matter field content: the Standard Weyl multiplet and the Dilaton Weyl multiplet.	result 0.87	0.92	0.43	asserted 1.00
s2	At the linearized level we obtain the transformation rules for the Dilaton Weyl multiplet by coupling it to the multiplet of currents corresponding to an on-shell vector multiplet.	method 0.70	0.95	0.06	asserted 1.00
s3	We construct the full non-linear transformation rules for both multiplets by gauging the D=5 superconformal algebra F^2(4).	method 0.51	0.96	0.24	asserted 1.00
s4	We show that the Dilaton Weyl multiplet can also be obtained by solving the equations of motion for an improved vector multiplet coupled to the Standard Weyl multiplet.	result 0.86	0.92	0.16	asserted 1.00

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References

Works cited (41)

[5]

M. Nishimura, Conformal supergravity from the AdS/CFT correspondence, Nucl. Phys. B588 (2000) 471–482, hep-th/0004179. 36

View on Pith Pith review arXiv 2000
[41]

T. Fujita and K. Ohashi, Superconformal tensor calculus in ﬁve dimensions, hep-th/0104130. 39

View on Pith Pith review arXiv
[1]

A. Salam and E. Sezgin, Supergravities in diverse dimensions. vol. 1, 2 , North-Holland 1989

View on Pith 1989
[2]

M. Kaku and P.K. Townsend, Poincar´ e supergravity as broken superconformal gravity, Phys. Lett. B76 (1978) 54

View on Pith 1978
[3]

L. Randall and R. Sundrum, An alternative to compactiﬁcation , Phys. Rev. Lett. 83 (1999) 4690–4693, hep-th/9906064

View on Pith Pith review arXiv 1999
[4]

L. Randall and R. Sundrum, A large mass hierarchy from a small extra dimension, Phys. Rev. Lett. 83 (1999) 3370–3373, hep-ph/9905221

View on Pith Pith review arXiv 1999
[6]

R. D’Auria, S. Ferrara and S. Vaula, Matter coupled F (4) supergravity and the AdS6/CFT 5 correspondence, JHEP 10 (2000) 013, hep-th/0006107

View on Pith Pith review arXiv 2000
[7]

V. Balasubramanian, E. Gimon, D. Minic and J. Rahmfeld, Four dimensional conformal supergravity from AdS space , hep-th/0007211

View on Pith Pith review arXiv
[8]

R. Kallosh and A. Linde, Supersymmetry and the brane world , JHEP 02 (2000) 005, hep-th/0001071

View on Pith Pith review arXiv 2000
[9]

K. Behrndt and M. Cvetiˇ c, Anti-de Sitter vacua of gauged supergravities with 8 supercharges , Phys. Rev. D61 (2000) 101901, hep-th/0001159

View on Pith Pith review arXiv 2000
[10]

A. Ceresole and G. Dall’Agata, General matter coupled N = 2, D = 5 gauged supergravity, Nucl. Phys. B585 (2000) 143–170, hep-th/0004111

View on Pith Pith review arXiv 2000
[11]

M. G¨ unaydin, G. Sierra and P.K. Townsend, The geometry of N = 2 Maxwell–Einstein supergravity and Jordan algebras , Nucl. Phys. B242 (1984) 244

View on Pith 1984
[12]

M. G¨ unaydin, G. Sierra and P.K. Townsend, Gauging the d = 5 Maxwell–Einstein supergravity theories: more on Jordan al gebras, Nucl. Phys. B253 (1985) 573

View on Pith 1985
[13]

E. Bergshoeﬀ, R. Kallosh and A. Van Proeyen, Supersymmetry in singular spaces, JHEP 10 (2000) 033, hep-th/0007044

View on Pith Pith review arXiv 2000
[14]

K. Behrndt, C. Herrmann, J. Louis and S. Thomas, Domain walls in ﬁve dimensional supergravity with non- trivial hypermulti plets, JHEP 01 (2000) 011, hep-th/0008112

View on Pith Pith review arXiv 2000
[15]

K. Behrndt and M. Cvetiˇ c, Gauging of N = 2 supergravity hypermultiplet and novel renormalization group ﬂows , to be published in Nucl. Phys. B, hep-th/0101007

View on Pith Pith review arXiv
[16]

K. Behrndt, S. Gukov and M. Shmakova, Domain walls, black holes, and supersymmetric quantum mechanics , hep-th/0101119. 37

View on Pith Pith review arXiv
[17]

A. Ceresole, G. Dall’Agata, R. Kallosh and A. Van Proeyen, Hypermultiplets, domain walls and supersymmetric attract ors, to be published in Phys. Rev. D, hep-th/0104056

View on Pith Pith review arXiv
[18]

B. de Wit, M. Roˇ cek and S. Vandoren, Hypermultiplets, hyperk¨ ahler cones and quaternion-K¨ ahler geometry, JHEP 02 (2001) 039, hep-th/0101161

View on Pith Pith review arXiv 2001
[19]

M. Kaku, P.K. Townsend and P. van Nieuwenhuizen, Gauge theory of the conformal and superconformal group , Phys. Lett. B69 (1977) 304–308

View on Pith 1977
[20]

M. Kaku, P.K. Townsend and P. van Nieuwenhuizen, Properties of conformal supergravity, Phys. Rev. D17 (1978) 3179

View on Pith 1978
[21]

S. Ferrara, M. Kaku, P.K. Townsend and P. van Nieuwenhuizen, Uniﬁed ﬁeld theories with U(N) internal symmetries: gauging the superconformal group, Nucl. Phys. B129 (1977) 125

View on Pith 1977
[22]

E. Bergshoeﬀ, E. Sezgin and A. Van Proeyen, Superconformal tensor calculus and matter couplings in six dimensions , Nucl. Phys. B264 (1986) 653

View on Pith 1986
[23]

T. Kugo and K. Ohashi, Supergravity tensor calculus in 5D from 6D, Prog. Theor. Phys. 104 (2000) 835–865, hep-ph/0006231

View on Pith Pith review arXiv 2000
[24]

A. Van Proeyen, Tools for supersymmetry , hep-th/9910030. in Annals of the University of Craiova, Physics AUC, Volume 9 (part I) 1999, pp.1–48

View on Pith Pith review arXiv 1999
[25]

P. Howe and U. Lindstrom, The supercurrent in ﬁve-dimensions , Phys. Lett. B103 (1981) 422–426

View on Pith 1981
[26]

S. Ferrara and B. Zumino, Transformation properties of the supercurrent, Nucl. Phys. B87 (1975) 207

View on Pith 1975
[27]

M.F. Sohnius, The multiplet of currents for N = 2 extended supersymmetry, Phys. Lett. B81 (1979) 8

View on Pith 1979
[28]

E. Bergshoeﬀ, M. de Roo and B. de Wit, Extended conformal supergravity, Nucl. Phys. B182 (1981) 173. 38

View on Pith 1981
[29]

E. Bergshoeﬀ, E. Sezgin and A. Van Proeyen, (2,0) tensor multiplets and conformal supergravity in D = 6, Class. Quant. Grav. 16 (1999) 3193–3206, hep-th/9904085

View on Pith Pith review arXiv 1999
[30]

E. Bergshoeﬀ and M. de Roo, The supercurrent in ten-dimensions , Phys. Lett. B112 (1982) 53

View on Pith 1982
[31]

B. de Wit, J.W. van Holten and A. Van Proeyen, Transformation rules of N = 2 supergravity multiplets, Nucl. Phys. B167 (1980) 186

View on Pith 1980
[32]

L. J. Romans, The F (4) gauged supergravity in six-dimensions , Nucl. Phys. B269 (1986) 691

View on Pith 1986
[33]

J. W. van Holten and A. Van Proeyen, N = 1 supersymmetry algebras in d = 2, 3, 4 mod. 8 , J. Phys. A15 (1982) 3763

View on Pith 1982
[34]

R. D’Auria, S. Ferrara, M.A. Lledo and V.S. Varadarajan, Spinor algebras, hep-th/0010124

View on Pith Pith review arXiv
[35]

E. Bergshoeﬀ, M. de Roo and B. de Wit, Conformal supergravity in ten dimensions , Nucl. Phys. B217 (1983) 489

View on Pith 1983
[36]

W. Nahm, Supersymmetries and their representations , Nucl. Phys. B135 (1978) 149

View on Pith 1978
[37]

M. Zucker, Minimal oﬀ-shell supergravity in ﬁve dimensions , Nucl. Phys. B570 (2000) 267–283, hep-th/9907082

View on Pith Pith review arXiv 2000
[38]

P. Howe, Oﬀ-shell N = 2 and N = 4 supergravity in ﬁve-dimensions , CERN-TH-3181

View on Pith
[39]

E. Cremmer, Supergravities in 5 dimensions , invited paper at the Nuﬃeld Gravity Workshop, Cambridge, England, Jun 22–Jul 12, 198 0

View on Pith
[40]

K. Behrndt and M. Cvetiˇ c, Supersymmetric domain wall world from D = 5 simple gauged supergravity, Phys. Lett. B475 (2000) 253–260, hep-th/9909058

View on Pith Pith review arXiv 2000

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Higher Derivative Corrections and Central Charges from Wrapped M5-branes
hep-th 2014-08 accept novelty 6.0 of 10

Four-derivative supergravity corrections to wrapped M5-brane geometries reproduce the subleading 1/N central charges of the dual field theories exactly.
5-dim Superconformal Index with Enhanced En Global Symmetry
hep-th 2012-06 conditional novelty 6.0 of 10

The five-dimensional Sp(1) superconformal index, computed by localization including instantons, organizes into E_{N_f+1} characters for N_f up to 5, confirming the conjectured exceptional global symmetry enhancement.
Six-dimensional Supergravity and Projective Superfields
hep-th 2012-04 conditional novelty 6.0 of 10

A superspace geometry and projective action principle for six-dimensional N=(1,0) conformal supergravity are constructed, extending the projective superspace program to six dimensions.
Near-horizon analysis of D=5 BPS black holes and rings
hep-th 2009-10 conditional novelty 6.0 of 10

Using only near-horizon data and off-shell superconformal calculus, the authors derive a universal Wald entropy formula for five-dimensional BPS black holes and rings with curvature-squared corrections, and show the r...
Supersymmetric Completion of an R^2 Term in Five-Dimensional Supergravity
hep-th 2006-11 accept novelty 6.0 of 10

The authors derive the bosonic supersymmetric completion of the mixed gauge-gravitational Chern-Simons term in 5D N=2 supergravity and show its AdS vacuum condition reproduces 4D a-maximization.
Higher derivative effects on eta/s at finite chemical potential
hep-th 2009-03 accept novelty 5.0 of 10

With four-derivative supersymmetric corrections, eta/s = (1/4π)[1 - ((c-a)/a)(1+q)], so a nonzero R-charge chemical potential increases the violation of the KSS bound rather than reducing it.
N=2 supergravity in five dimensions revisited
hep-th 2004-03 conditional novelty 5.0 of 10

The authors gauge-fix the superconformal N=2, D=5 theory to obtain the general Poincare action with vector, tensor and hypermultiplets, including off-diagonal vector-tensor couplings previously claimed impossible.
Embedding formalism for anti-de Sitter superspaces
hep-th 2026-05 unverdicted novelty 4.0 of 10

Develops bi-supertwistor realizations and extensions for N-extended AdS superspaces in 4D/5D with supergravity correspondence and superparticle applications.
On conformal supergravity and projective superspace
hep-th 2009-05 accept novelty 4.0 of 10

The paper derives the finite super-Weyl transformations of Howe's N=2 conformal supergravity and shows they reduce to the authors' earlier projective superspace formulation after gauge fixing.
${\cal N}=2$ Supergravity in $D=4,5,6$ Dimensions
hep-th 2020-04 accept novelty 2.0 of 10

A book-length, self-contained account of how N=2 supergravity in D=4,5,6 is constructed by superconformal methods, and of the special and quaternionic-Kahler geometries that the scalar sectors realise.

How the literature uses it

43 arXiv papers cite this in 96 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 62 sentences without a confident label

Uses its method or tool 5 papers

To avoid these issues, we instead make use of supersymmetry, and in particular the result of [ref] , which worked out the supersymmetric completion of the $A∧ R∧R$ term in $𝒩=2$ supergravity coupled to an arbitrary number of vector multiplets using the superconformal tensor calculus methods developed in [ref] .

Black holes in five-dimensional gauged supergravity with higher derivatives · Introduction · 0.82
To construct the 4d dilaton Weyl multiplet, we will follow the same procedure used in in five dimensions [ref] : we couple an $N=2$ vector multiplet to the standard Weyl multiplet and use the equations of motion to eliminate the auxiliary fields.

$N=2$ dilaton Weyl multiplet in 4D supergravity · The standard Weyl multiplet and its (un)conventional constraints · 0.93
Upon setting the gauginos as well as the $M$ and $Y_ij$ scalar to zero, the only non-trivial supersymmetry variation is [ref]

Supersymmetrizing 5d instanton operators · Supersymmetric Yang monopoles in five-dim. gauge theories · 0.81

Compares with it 4 papers

For signature $(1,4)$ the resulting reality properties of symplectic Majorana spinor bilinears and supersymmetry variations agree with [ref] and [ref] .

Five-dimensional vector multiplets in arbitrary signature · Supersymmetry variations · 0.99
Note that this is a feature which is absent in the constructions of half-maximally supersymmetric dilaton Weyl multiplets [ref] .

Torus reduction of maximal conformal supergravity · Gauge fixing the R-symmetry group · 0.96
In four and five dimensions [ref] the Weyl 1 multiplet can be used as an independent multiplet to construct a pure Poincaré action, not leading to inconsistencies and having proper kinetic terms for the matter fields.

Off-shell N=(1,0), D=6 supergravity from superconformal methods · Conclusions · 0.94

Cites it as background 19 papers

The dilaton Weyl multiplet was known for the minimal conformal supergravity in five and six dimensions since long [ref] and was recently discovered in $N=2$ conformal supergravity four dimensions [ref] .

Curvature squared action in four dimensional $N=2$ supergravity using the dilaton Weyl multiplet · Introduction · 0.91
Most of the results presented in this and the next section can be found in [ref] .

Off-shell D=5, N=2 Riemann Squared Supergravity · Conformal Multiplets · 0.97
The dilaton Weyl multiplets have also been constructed for various dimensions and supersymmetries such as for $N=1$ conformal supergravity in five dimensions in [ref] , $(1,0)$ conformal supergravity in six dimensions [ref] , $N=2$ conformal supergravity in five dimensions [ref] as well as $N=4$ conformal supergravity in four dimensions [ref] .

$SU(2)\times SU(2)$ dilaton Weyl multiplets for maximal conformal supergravity in four, five, and six dimensions · Introduction · 0.81

Discussion

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[1] [5]

M. Nishimura, Conformal supergravity from the AdS/CFT correspondence, Nucl. Phys. B588 (2000) 471–482, hep-th/0004179. 36

View on Pith Pith review arXiv 2000

[2] [41]

T. Fujita and K. Ohashi, Superconformal tensor calculus in ﬁve dimensions, hep-th/0104130. 39

View on Pith Pith review arXiv

[3] [1]

A. Salam and E. Sezgin, Supergravities in diverse dimensions. vol. 1, 2 , North-Holland 1989

View on Pith 1989

[4] [2]

M. Kaku and P.K. Townsend, Poincar´ e supergravity as broken superconformal gravity, Phys. Lett. B76 (1978) 54

View on Pith 1978

[5] [3]

L. Randall and R. Sundrum, An alternative to compactiﬁcation , Phys. Rev. Lett. 83 (1999) 4690–4693, hep-th/9906064

View on Pith Pith review arXiv 1999

[6] [4]

L. Randall and R. Sundrum, A large mass hierarchy from a small extra dimension, Phys. Rev. Lett. 83 (1999) 3370–3373, hep-ph/9905221

View on Pith Pith review arXiv 1999

[7] [6]

R. D’Auria, S. Ferrara and S. Vaula, Matter coupled F (4) supergravity and the AdS6/CFT 5 correspondence, JHEP 10 (2000) 013, hep-th/0006107

View on Pith Pith review arXiv 2000

[8] [7]

V. Balasubramanian, E. Gimon, D. Minic and J. Rahmfeld, Four dimensional conformal supergravity from AdS space , hep-th/0007211

View on Pith Pith review arXiv

[9] [8]

R. Kallosh and A. Linde, Supersymmetry and the brane world , JHEP 02 (2000) 005, hep-th/0001071

View on Pith Pith review arXiv 2000

[10] [9]

K. Behrndt and M. Cvetiˇ c, Anti-de Sitter vacua of gauged supergravities with 8 supercharges , Phys. Rev. D61 (2000) 101901, hep-th/0001159

View on Pith Pith review arXiv 2000

[11] [10]

A. Ceresole and G. Dall’Agata, General matter coupled N = 2, D = 5 gauged supergravity, Nucl. Phys. B585 (2000) 143–170, hep-th/0004111

View on Pith Pith review arXiv 2000

[12] [11]

M. G¨ unaydin, G. Sierra and P.K. Townsend, The geometry of N = 2 Maxwell–Einstein supergravity and Jordan algebras , Nucl. Phys. B242 (1984) 244

View on Pith 1984

[13] [12]

M. G¨ unaydin, G. Sierra and P.K. Townsend, Gauging the d = 5 Maxwell–Einstein supergravity theories: more on Jordan al gebras, Nucl. Phys. B253 (1985) 573

View on Pith 1985

[14] [13]

E. Bergshoeﬀ, R. Kallosh and A. Van Proeyen, Supersymmetry in singular spaces, JHEP 10 (2000) 033, hep-th/0007044

View on Pith Pith review arXiv 2000

[15] [14]

K. Behrndt, C. Herrmann, J. Louis and S. Thomas, Domain walls in ﬁve dimensional supergravity with non- trivial hypermulti plets, JHEP 01 (2000) 011, hep-th/0008112

View on Pith Pith review arXiv 2000

[16] [15]

K. Behrndt and M. Cvetiˇ c, Gauging of N = 2 supergravity hypermultiplet and novel renormalization group ﬂows , to be published in Nucl. Phys. B, hep-th/0101007

View on Pith Pith review arXiv

[17] [16]

K. Behrndt, S. Gukov and M. Shmakova, Domain walls, black holes, and supersymmetric quantum mechanics , hep-th/0101119. 37

View on Pith Pith review arXiv

[18] [17]

A. Ceresole, G. Dall’Agata, R. Kallosh and A. Van Proeyen, Hypermultiplets, domain walls and supersymmetric attract ors, to be published in Phys. Rev. D, hep-th/0104056

View on Pith Pith review arXiv

[19] [18]

B. de Wit, M. Roˇ cek and S. Vandoren, Hypermultiplets, hyperk¨ ahler cones and quaternion-K¨ ahler geometry, JHEP 02 (2001) 039, hep-th/0101161

View on Pith Pith review arXiv 2001

[20] [19]

M. Kaku, P.K. Townsend and P. van Nieuwenhuizen, Gauge theory of the conformal and superconformal group , Phys. Lett. B69 (1977) 304–308

View on Pith 1977

[21] [20]

M. Kaku, P.K. Townsend and P. van Nieuwenhuizen, Properties of conformal supergravity, Phys. Rev. D17 (1978) 3179

View on Pith 1978

[22] [21]

S. Ferrara, M. Kaku, P.K. Townsend and P. van Nieuwenhuizen, Uniﬁed ﬁeld theories with U(N) internal symmetries: gauging the superconformal group, Nucl. Phys. B129 (1977) 125

View on Pith 1977

[23] [22]

E. Bergshoeﬀ, E. Sezgin and A. Van Proeyen, Superconformal tensor calculus and matter couplings in six dimensions , Nucl. Phys. B264 (1986) 653

View on Pith 1986

[24] [23]

T. Kugo and K. Ohashi, Supergravity tensor calculus in 5D from 6D, Prog. Theor. Phys. 104 (2000) 835–865, hep-ph/0006231

View on Pith Pith review arXiv 2000

[25] [24]

A. Van Proeyen, Tools for supersymmetry , hep-th/9910030. in Annals of the University of Craiova, Physics AUC, Volume 9 (part I) 1999, pp.1–48

View on Pith Pith review arXiv 1999

[26] [25]

P. Howe and U. Lindstrom, The supercurrent in ﬁve-dimensions , Phys. Lett. B103 (1981) 422–426

View on Pith 1981

[27] [26]

S. Ferrara and B. Zumino, Transformation properties of the supercurrent, Nucl. Phys. B87 (1975) 207

View on Pith 1975

[28] [27]

M.F. Sohnius, The multiplet of currents for N = 2 extended supersymmetry, Phys. Lett. B81 (1979) 8

View on Pith 1979

[29] [28]

E. Bergshoeﬀ, M. de Roo and B. de Wit, Extended conformal supergravity, Nucl. Phys. B182 (1981) 173. 38

View on Pith 1981

[30] [29]

E. Bergshoeﬀ, E. Sezgin and A. Van Proeyen, (2,0) tensor multiplets and conformal supergravity in D = 6, Class. Quant. Grav. 16 (1999) 3193–3206, hep-th/9904085

View on Pith Pith review arXiv 1999

[31] [30]

E. Bergshoeﬀ and M. de Roo, The supercurrent in ten-dimensions , Phys. Lett. B112 (1982) 53

View on Pith 1982

[32] [31]

B. de Wit, J.W. van Holten and A. Van Proeyen, Transformation rules of N = 2 supergravity multiplets, Nucl. Phys. B167 (1980) 186

View on Pith 1980

[33] [32]

L. J. Romans, The F (4) gauged supergravity in six-dimensions , Nucl. Phys. B269 (1986) 691

View on Pith 1986

[34] [33]

J. W. van Holten and A. Van Proeyen, N = 1 supersymmetry algebras in d = 2, 3, 4 mod. 8 , J. Phys. A15 (1982) 3763

View on Pith 1982

[35] [34]

R. D’Auria, S. Ferrara, M.A. Lledo and V.S. Varadarajan, Spinor algebras, hep-th/0010124

View on Pith Pith review arXiv

[36] [35]

E. Bergshoeﬀ, M. de Roo and B. de Wit, Conformal supergravity in ten dimensions , Nucl. Phys. B217 (1983) 489

View on Pith 1983

[37] [36]

W. Nahm, Supersymmetries and their representations , Nucl. Phys. B135 (1978) 149

View on Pith 1978

[38] [37]

M. Zucker, Minimal oﬀ-shell supergravity in ﬁve dimensions , Nucl. Phys. B570 (2000) 267–283, hep-th/9907082

View on Pith Pith review arXiv 2000

[39] [38]

P. Howe, Oﬀ-shell N = 2 and N = 4 supergravity in ﬁve-dimensions , CERN-TH-3181

View on Pith

[40] [39]

E. Cremmer, Supergravities in 5 dimensions , invited paper at the Nuﬃeld Gravity Workshop, Cambridge, England, Jun 22–Jul 12, 198 0

View on Pith

[41] [40]

K. Behrndt and M. Cvetiˇ c, Supersymmetric domain wall world from D = 5 simple gauged supergravity, Phys. Lett. B475 (2000) 253–260, hep-th/9909058

View on Pith Pith review arXiv 2000