Batalin-Vilkovisky formulation of the $\mathcal N=1$ supergravity in ten dimensions

Charles Strickland-Constable; Fridrich Valach; Julian Kupka

REVIEW 4 major objections 5 minor 38 references

Batalin-Vilkovisky formulation of the $\mathcal N=1$ supergravity in ten dimensions

T0 review · 4 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read The paper claims that ten-dimensional $\mathcal{N}=1$ supergravity coupled to Yang–Mills multiplets admits a full Batalin–Vilkovisky action, written explicitly as equation (19) in the component field formalism.

desk verdict A genuinely new BV action for N=1 D=10 supergravity, but the classical master equation is explicitly unproven—treat it as a strong conjecture, and send it to referees who can check it. read the letter →

arxiv 2501.18008 v1 pith:BDHRR22V submitted 2025-01-29 hep-th

Julian Kupka , Charles Strickland-Constable , Fridrich Valach This is my paper · ORCID

classification hep-th PACS 04.65.+e

keywords Batalin-VilkoviskyformalismN=1supergravitytendimensionsYang-Millsmultipletscomponentfieldclassicalmasterequationgeneralisedgeometrytwisting

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper presents a complete Batalin–Vilkovisky action for ten-dimensional $\mathcal{N}=1$ supergravity coupled to Yang–Mills multiplets, written directly in the component field formalism. The central object is a single local action functional, equation (19), defined on an extended field space that includes ghosts for supersymmetry, diffeomorphisms, and their reducibility, together with the corresponding antifields. If the action is correct, it gives the first background-independent BV description of a higher-dimensional supergravity, providing a standard starting point for quantisation and for constructing twists of the theory. The authors stress that they have not supplied a complete proof that the action satisfies the classical master equation; they provide structural checks and the matching $G=1$ limit, and leave the full proof to future work.

What carries the argument

The central machinery is the Batalin–Vilkovisky formalism itself, a framework for dealing with reducible gauge symmetries during quantisation, applied to the field space $T^*[-1]S$ described in the paper. The load-bearing construction is the vector bundle $S\to \mathcal{M}\times H^*$: a point is a generalised metric $G$, an invertible half-density $\sigma$, the fermions $\rho,\psi$, and the ghosts $e,\xi,f$, plus their antifields. The crucial mechanism is that the fermions live in bundles $S_\pm$ that themselves depend on $G$, so the field space carries a connection whose curvature (8) contributes an effective Lorentz term to the commutator of supersymmetries. This is what removes the Lorentz transformations from the algebra and keeps the BV action comparatively simple. The action (19) is then assembled by the standard BV dictionary: linear antifield terms encode the gauge transformations and symmetry algebra, and quadratic antifield terms encode the failure of the algebra to close off shell.

What would settle it

Compute the BV antibracket $(S,S)$ of the action (19); if any coefficient, at any order in the antifields, is nonzero, the central claim is false. Because the action is a finite sum of local monomials, this is a finite symbolic computation that would settle the matter.

Watch

Extended reading notes

Core claim

The paper claims that equation (19) is the full BV extension of the classical $\mathcal{N}=1$, $D=10$ supergravity action (9), including the super Yang–Mills sector. The field space is $T^*[-1]S$, where $S$ is a vector bundle over the space of generalised metrics and half-densities; its fibre contains the fermionic fields $\rho$ and $\psi$, the supersymmetry ghost $e$, the diffeomorphism ghost $\xi$, and the ghost-for-ghost $f$. The action combines the classical terms with the supersymmetry and diffeomorphism transformations of the fields, the structure coefficients of the off-shell symmetry algebra, and antifield terms that measure the failure of the algebra to close off shell. The authors verify that at $G=1$ the expression reduces to the known BV action of dilatonic supergravity and that the overall structure matches the $D=4$ BV analysis, but they explicitly leave a full proof of the classical master equation for future work.

Load-bearing premise

The whole construction depends on equation (19) satisfying the classical master equation $(S,S)=0$, which the authors state they have not fully proved; if that identity fails, (19) is not a valid BV action.

Editorial extensions

If this is right

If equation (19) satisfies the classical master equation, it is the first BV action for a higher-dimensional supergravity in the background-independent component field formalism.
The action provides the component-field starting point for the Costello–Li twist of type I supergravity, putting the conjectured relation to BCOV theory on a firmer footing.
The $G=1$ reduction reproduces the BV action of dilatonic supergravity, so the ghost-for-ghost structure for the B-field reducibility is already fixed.
Proceeding from this action, one can look for perturbative solutions of the quantum master equation to probe quantum corrections to the theory.
Consistent truncations should produce BV actions for lower-dimensional supergravities.

Reading between the lines

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

One way to close the gap left by the paper would be a direct computer-algebra verification of $(S,S)=0$ for equation (19); the authors mention having run lengthy checks, so the computation appears feasible.
The critical-point equation $D_\alpha e = \frac{1}{16}\sigma^{-2}e(\bar\psi^*_\alpha e)$ suggests a larger class of supersymmetric backgrounds when antifields are active, beyond the usual parallel-spinor conditions that yield Calabi–Yau spaces.
A deformation argument from the $G=1$ topological sector might supply the missing proof of the master equation, treating the generalised metric deformation as a perturbation; this route is not attempted in the paper.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Julian, here's my read on Kupka-Strickland-Constable-Valach, arXiv:2501.18008.

The genuinely new thing is an explicit BV action, eq (19), for N=1 D=10 supergravity coupled to Yang-Mills, in the component-field formalism. As far as I know, that's a first—previous BV constructions were D=4 or pure spinor superfield. The generalized-geometry packaging is clean, and the action has a nice structure: the anti-field terms are largely determined by the supersymmetry variations and the failure of the algebra to close off-shell. The G=1 limit reproducing their earlier dilatonic supergravity BV action is a real, nontrivial check. The potential payoff is also clear: this gives the starting point for the Costello-Li twisted supergravity program in the component formalism.

But the central identity is not proved. The classical master equation (S,S)=0 for (19) is exactly what makes it a BV action, and the authors state plainly that they don't give a full proof and leave it to future work. That's not a minor omission. The consistency checks they offer—matching the G=1 limit and structural similarity to D=4—are suggestive but don't test all sectors of the master equation; the curvature terms in (4) and (8) are frozen in the G=1 limit. They also mention 'additional nontrivial checks' that are too lengthy to report, which is unsatisfying because no one can assess them.

There's a second deferred proof: the supersymmetry algebra (13), whose details are also postponed. So the paper is really a well-motivated conjecture with strong circumstantial evidence, not an established result. The authors are upfront about what is proved and what isn't, but a reader should not walk away thinking eq (19) has been verified.

That said, the paper deserves serious engagement. The construction is novel, the authors are credible (their prior work establishes the framework), and the result is important enough that referees should spend time checking it. My recommendation: send it to peer review, and push the authors to provide the full master-equation proof, either in the paper or an accompanying note. If the proof is too long for a letter, that's fine, but then the paper should be framed as a conjectural BV action, with the proof to follow.

I'd cite this if I worked in the area, and I'd bring it to reading group. Serious thinker: yes.

Referee Report

4 major / 5 minor

Summary. The paper presents a Batalin-Vilkovisky (BV) action for ten-dimensional N=1 supergravity coupled to Yang-Mills multiplets, written in the component field formalism and organized with the help of generalized geometry. The classical field space is a vector bundle over the space of generalized metrics and half-densities; the paper specifies the ghost and antifield content and proposes the BV action in Eq. (19). The authors offer as evidence that the action reproduces the known BV formulation of dilatonic supergravity in the G=1 limit, structurally matches the D=4 BV analysis of Baulieu et al., and passes additional checks that are not reported. They explicitly state that the classical master equation (S,S)=0 is not proved and defer a complete proof to future work. The paper ends with a discussion of critical points of the BV action and a suggested link to the Costello-Li twist of supergravity.

Significance. If Eq. (19) indeed satisfies the classical master equation, this would be the first BV construction of a higher-dimensional supergravity in the background-independent component formalism, as opposed to pure spinor superfield approaches. The construction is elegant and parameter-free, and it leverages the authors' earlier generalized-geometric formulation to simplify the field space and the supersymmetry algebra. The proposed BV action also provides a concrete starting point for studying quantization and the Costello-Li twist. However, the central defining property of a BV action, the classical master equation, is not established in the manuscript; the correctness of Eq. (19) therefore remains a well-motivated conjecture rather than a demonstrated result.

major comments (4)

[BV action, after Eq. (19)] The paper states that 'checking explicitly that it satisfies the classical master equation is not easy', that the authors 'do not give a full proof of this fact', and that 'a complete proof is left for a future work'. In the BV formalism, the classical master equation is the defining consistency condition; without it, Eq. (19) cannot be claimed to be the BV action of the theory. The checks listed (the G=1 dilatonic limit and the structural match to D=4 supergravity) are suggestive but do not cover all sectors of the master equation, such as the terms quadratic in antifields or the curvature-dependent terms. The central claim of the paper therefore needs either a proof of (S,S)=0 or an explicit reframing of Eq. (19) as a conjecture, with the title and abstract adjusted accordingly.
[BV action and G=1 limit] The G=1 limit freezes the generalized metric and therefore cannot test the field-space curvature terms in Eqs. (4) and (8), nor the covariant derivatives in Eq. (19) that depend on this curvature. These terms enter directly into the master equation through the horizontal/vertical splitting of T*[-1]S, so the claimed 'important nontrivial check' does not constrain an essential part of (S,S). To make the claim load-bearing, the authors should provide at least a partial verification of the master equation in the sectors involving G* and the curvature-dependent terms, or give a systematic argument showing why the G=1 limit is sufficient.
[Supersymmetry algebra, Eqs. (10)-(13)] The BV action is explicitly built from the supersymmetry algebra, including the 'structure coefficients' and the failure of the algebra to close off-shell. The algebra is quoted in Eqs. (11)-(13) with the details postponed to a future work [21]. Since the consistency of the BV action depends on the precise form of these identities, the paper should either include the essential parts of the calculation or state explicitly which terms in Eq. (19) would need to be modified if the quoted algebra were changed. As written, the derivation of the ghost and antifield terms in (19) is not fully documented.
[BV action, 'additional nontrivial checks'] The sentence 'even after performing additional nontrivial checks (which are too lengthy to report on here)' is not verifiable by the reader. If these checks are part of the evidence for the central claim, they should be included in an appendix or a supplementary file; otherwise the reader cannot assess whether they constrain the missing sectors of the master equation.

minor comments (5)

[Abstract] There is a typo in the abstract: 'componen t field formalism' should be 'component field formalism'.
[Introduction] The phrase 'apriori' should be written as 'a priori', and 'Lichnerowitz' in the Conclusions should be 'Lichnerowicz'.
[Fermions and supersymmetry, Eq. (5) vs. BV field space, Eqs. (15)-(16)] Eq. (5) defines the gravitino as ψ ∈ Γ(Π S− ⊗ C− ⊗ H), while Eqs. (15) and (16) list ψ ∈ Γ(Π S− ⊗ C+ ⊗ H). This is an apparent inconsistency in the field content. Please clarify which bundle is intended, or correct the typo.
[Conclusions] The phrase 'FevenBV' should be typeset as a mathematical expression, e.g., F_BV^even, for readability.
[Appendix, Eq. (25)] The sentence introducing Eq. (25) says 'the equations are easy to find and are shown in (25)' but the displayed system is not explicitly labeled as (25) in the text; please ensure the numbering is consistent.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: equation (19) is presented as a new BV action assembled from the classical action and symmetry variations, not as a re-labeling of those inputs; the deferred proof of the classical master equation is an incompleteness in validation, not a circular reduction.

full rationale

The claimed result, the BV action (19), is not defined in terms of the property it is supposed to have. The paper starts from the classical action (9) and the supersymmetry and diffeomorphism transformations (10) and (13), and assembles (19) by the standard BV prescription: linear antifield terms from the transformations, quadratic antifield terms from their off-shell failure to close, and ghost-for-ghost terms from reducibility. These inputs come substantially from the same authors' prior work ([4] and [10]), so there is a self-citation burden, but the cited results are used as ingredients, not as a proof that (19) satisfies the master equation. Indeed the paper explicitly states the master equation is not proved: 'Consequently we do not give a full proof of this fact' and 'A complete proof is left for a future work.' That is a genuine gap in establishing the central claim, but it is not circularity: no fitted parameter is renamed a prediction, no equation is equivalent to its own target by construction, and no uniqueness claim from the authors is used to exclude alternatives. The appendix's critical-point analysis starts from (19) and does not assume the master equation. Score 2 reflects the minor but real dependence on the authors' prior results and the deferred consistency proof, while the construction itself is not circular.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

The central claim rests on earlier generalized-geometric formulations of the action and symmetries, mostly by the same authors, and on the unproved master-equation identity. No numeric free parameters or new physical entities are introduced; the ghosts e, xi, and f are standard BV ghosts.

assumptions (4)

domain assumption The generalized-geometric action S0 (Eq 9) correctly describes N=1 D=10 supergravity coupled to Yang-Mills, with the supersymmetry variations (10).
The BV construction starts from this action and these variations; correctness is imported from earlier work [4] by the same authors.
domain assumption The supersymmetry algebra commutator (13) is as stated, closing on-shell without Lorentz terms, based on the curvature (8).
This algebra is used to read off the ghost couplings in (19); the calculation is lengthy and deferred to future work [21].
domain assumption The field-space vector-bundle connection and curvature formulas (4) and (8) are correct.
These formulas justify the horizontal/vertical splitting of the BV field space and the simplification of the supersymmetry commutator.
domain assumption The BV action for the topological dilatonic supergravity limit [10] is correct and can be used to fix the ghost-for-ghost terms in (19).
The paper uses the G=1 limit to determine f-dependent terms; [10] is prior work by the same authors.

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Cite this review

Pith. "Pith review of Batalin-Vilkovisky formulation of the $\mathcal N=1$ supergravity in ten dimensions." pith.science (2026). https://pith.science/paper/BDHRR22V

@misc{pith2026250118008,
  author       = {Pith},
  title        = {Pith review of: Batalin-Vilkovisky formulation of the $\mathcal N=1$ supergravity in ten dimensions},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BDHRR22V}},
  note         = {Machine review of arXiv:2501.18008}
}

abstract

We present a full Batalin-Vilkovisky action in the component field formalism for $\mathcal N=1$ supergravity in ten dimensions coupled to Yang-Mills multiplets.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

38 extracted references · 26 canonical work pages

[21]

Siegel, Phys

W. Siegel, Phys. Rev. D 48, 2826 (1993) , arXiv:hep-th/9305073

arXiv 1993
[1]

tautological

any C+ takes the form {x + (ixg +ixB − 1 2 TrAi xA) +ixA |x ∈TM } ⊂ E (2) for some Lorentzian metric g, Kalb–Ramond 2-form B, and G-connection 1-form A. The dilaton function φ is encoded in σ via σ2 = √ |g|e−2φ, (3) where √ |g| stands for the standard metric density. Consider now the “tautological” bundle C+ → M, whose ﬁber at G is the space Γ( C+). Any s...

work page
[2]

G. F. Chapline and N. S. Manton, Phys. Lett. B 120, 105 (1983)

work page 1983
[3]

M. Dine, R. Rohm, N. Seiberg, and E. Witten, Phys. Lett. B 156, 55 (1985)

work page 1985
[4]

Notably, since the formulas (

are relatively lengthy and involve a generous handful of Fierz identi- ties. Notably, since the formulas (

work page
[5]

Kupka, C

J. Kupka, C. Strickland-Constable, and F. Valach, On higher fermions in supergravity (2024), arXiv:2412.04968 [hep-th]

arXiv 2024
[6]

as they are not symmetries of the met- ric tensor formulation of the theory.) We postpone the details of the calculation to a future work [21]. BV FIELD SP ACE To construct the BV space we start with the classical ﬁeld space, add ghosts and ghosts for ghosts correspond- ing to local symmetries, and then adjoin the correspond- ing antiﬁelds. This yields th...

work page
[7]

Coimbra, C

A. Coimbra, C. Strickland-Constable, and D. Waldram, JHEP 11, 091 , arXiv:1107.1733 [hep-th]

arXiv

Show all 38 references

[8]

Garcia-Fernandez, Commun

M. Garcia-Fernandez, Commun. Math. Phys. 332, 89 (2014) , arXiv:1304.4294 [math.DG]

2014 arXiv
[9]

Following the usual BV machinery the form of this action is essentially read oﬀ from what was discussed be- fore: the linear terms in antiﬁelds include both (

is S = ∫ M Rσ2 + ¯ψα/Dψα + ¯ρ/Dρ + 2 ¯ρDαψα 4 − 1 768σ−2( ¯ψαγabcψα)(¯ργ abcρ) − 1 384σ−2( ¯ψαγabcψα)( ¯ψβγabcψβ) +σ∗[Lξσ − 1 8σ−1(¯ρe)] + G∗ aβ[(LξG)aβ + 1 2σ−2(¯eγaψβ)] + ¯ρ∗[Lξρ + /De + 1 192σ−2( ¯ψβγabcψβ)γabce] + ¯ψ∗ β[(Lξψ)β +Dβe + 1 8σ−2( ¯ψβρ)e (19) − 1 8σ−2( ¯ψβγae)γa...
[10]

This removes all the terms which look like Lorentz transformations and which would be present in the vielbein formulation

really correspond to horizontal and vertical parts of the vector ﬁeld δǫ on S0, the corresponding commutator on fermions picks up an extra term (in addition to the “naive” commutator of variations), coming from the curvature ( 8). This removes all the terms which look like Lor...
[11]

struc- ture coeﬃcients

and the generalised diﬀeomorphisms, as well as the “struc- ture coeﬃcients” of the symmetry algebra (ﬁrst part of the RHS of ( 13)), while the terms quadratic in antiﬁelds quantify the failure of the symmetries to close oﬀ-shell (last part of the RHS of ( 13)). Finally, an imp...
[12]

This can in particular be used to determine the terms in (

matches the BV action for the dilatonic supergrav- ity [10]. This can in particular be used to determine the terms in (
[13]

Consequently the BV action (

does not feature any Lorentz terms on the RHS as these are cancelled by the term coming from the nonzero curvature on this vector bundle. Consequently the BV action (
[14]

That being said, we note that although highly sugges- tive, the above arguments do not provide a full proof that the classical master equation is indeed satisﬁed

containing the ghost-for-ghost f , which ac- count for the reducibility of our description of generalised diﬀeomorphisms (which is the same regardless of whether G = 1 or not).[22] Our result also structurally matches the D = 4 supergravity BV analysis in [11]. That being said...
[15]

To summarise, our ﬁeld content up to now consists of G ∈ Γ(E∗ ⊗E) s.t

correspond to the fermionic ﬁelds ρ andψ, the supersymmetry ghost e, the diﬀeomorphism ghost ξ, and the ghost for ghost f , re- spectively. To summarise, our ﬁeld content up to now consists of G ∈ Γ(E∗ ⊗E) s.t. G2 = 1 and G∗ = G σ ∈ Γ(H) everywhere nonvanishing ρ ∈ Γ(Π S+ ⊗H) ...
[16]

The full proof of this fact is left for a future work

is incomplete or incorrect in any way and hence we are highly conﬁ- dent in its validity. The full proof of this fact is left for a future work. CONCLUSIONS AND OUTLOOK We have found the BV action for the N = 1 super- gravity in 10 dimensions, in general coupled to a super Yan...
[17]

The corresponding equations are easy to ﬁnd and are shown in ( 25)

(for any gauge group). The corresponding equations are easy to ﬁnd and are shown in ( 25). In particular setting to zero all the ﬁelds except for G, σ, and e these equations reduce to R aβ = /De =Dαe = ¯eγae = 0. (20) This is the condition for the background ( G,σ ) to be supe...
[18]

Bergshoeﬀ, M

E. Bergshoeﬀ, M. de Roo, B. de Wit, and P. van Nieuwen- huizen, Nucl. Phys. B 195, 97 (1982)

1982
[19]

Still, checking explicitly that it satisﬁes the classical master equation is not easy

is much simpler than one would apriori expect. Still, checking explicitly that it satisﬁes the classical master equation is not easy. Con- sequently we do not give a full proof of this fact but only provide various evidence in favour of its validity. A com- plete proof is left...
[20]

Kupka, C

J. Kupka, C. Strickland-Constable, and F. Valach, Direct derivation of gauged N = 1 supergravity in ten dimensions to all orders in fermions (2024), arXiv:2410.16046 [hep-th]

2024 arXiv
[22]

Coimbra, R

A. Coimbra, R. Minasian, H. Triendl, and D. Waldram, JHEP 11, 160 , arXiv:1407.7542 [hep-th]

arXiv
[23]

Kupka, C

J. Kupka, C. Strickland-Constable, and F. Valach, Super- gravity without gravity and its BV formulation (2024), arXiv:2408.14656 [hep-th]

2024 arXiv
[24]

Baulieu, M

L. Baulieu, M. P. Bellon, S. Ouvry, and J.-C. Wallet, Phys. Lett. B 252, 387 (1990)

1990
[25]

A. S. Cattaneo, N. Moshayedi, and A. S. Funcasta, 3D Supergravity In the Batalin–Vilkovisky Formalism (2024), arXiv:2412.14300 [hep-th]

2024 arXiv
[26]

A. S. Cattaneo and F. Fila-Robattino, BV-BFV descrip- tion of N = 1, D = 4 Supergravity, in preparation
[27]

Cederwall, Pure Spinors in Classical and Quantum Supergravity (2023) arXiv:2210.06141 [hep-th]

M. Cederwall, Pure Spinors in Classical and Quantum Supergravity (2023) arXiv:2210.06141 [hep-th]

2023 arXiv
[28]

Costello and S

K. Costello and S. Li, Adv. Theor. Math. Phys. 24, 1723 (2020) , arXiv:1905.09269 [hep-th]

2020 arXiv
[29]

Z.-J. Liu, A. Weinstein, and P. Xu, Journal of Diﬀerential Geometry 45, 547 (1997) , dg-ga/9508013

1997 arXiv
[30]

ˇSevera, Letters to Alan Weinstein about Courant al- gebroids (1998-2000), arXiv:1707.00265 [math.DG]

P. ˇSevera, Letters to Alan Weinstein about Courant al- gebroids (1998-2000), arXiv:1707.00265 [math.DG]

1998 arXiv
[31]

Any such connection also naturally acts on half-densities via Duσ = La(u)σ − 1 2 σ tr(Du), where L is the usual Lie derivative

A generalised connection is a map D : Γ( E) × Γ( E) → Γ( E) satisfying Df uv = f Duv, Du(f v) = f Duv + (a(u)f )v, and D⟨ · , · ⟩ = 0. Any such connection also naturally acts on half-densities via Duσ = La(u)σ − 1 2 σ tr(Du), where L is the usual Lie derivative
[32]

Garcia-Fernandez, Adv

M. Garcia-Fernandez, Adv. Math. 350, 1059 (2019) , arXiv:1611.08926 [math.DG]

2019 arXiv
[33]

In order to make sense of this one needs to provide the identiﬁcation of these two bundles, which is where the connection on S0 is used

In other words, notice that δǫρ corresponds to the dif- ference of two sections of two diﬀerent bundles (corre- sponding to G and G + δǫG, respectively). In order to make sense of this one needs to provide the identiﬁcation of these two bundles, which is where the connection o...
[34]

Kupka, C

J. Kupka, C. Strickland-Constable, and F. Valach, in preparation
[35]

As seen in [4] this corresponds reducibility of the gauge transformations of the B-ﬁeld
[36]

Costello and S

K. Costello and S. Li, Twisted supergravity and its quan- tization (2016), arXiv:1606.00365 [hep-th]

2016 arXiv
[37]

a conﬁguration with all odd ﬁelds vanishing

By a point we here mean a point in the even part Feven BV of the supermanifold FBV , i.e. a conﬁguration with all odd ﬁelds vanishing
[38]

Bershadsky, S

M. Bershadsky, S. Cecotti, H. Ooguri, and C. Vafa, Commun. Math. Phys. 165, 311 (1994) , arXiv:hep-th/9309140

1994 arXiv

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.

[1] [21]

Siegel, Phys

W. Siegel, Phys. Rev. D 48, 2826 (1993) , arXiv:hep-th/9305073

arXiv 1993

[2] [1]

tautological

any C+ takes the form {x + (ixg +ixB − 1 2 TrAi xA) +ixA |x ∈TM } ⊂ E (2) for some Lorentzian metric g, Kalb–Ramond 2-form B, and G-connection 1-form A. The dilaton function φ is encoded in σ via σ2 = √ |g|e−2φ, (3) where √ |g| stands for the standard metric density. Consider now the “tautological” bundle C+ → M, whose ﬁber at G is the space Γ( C+). Any s...

work page

[3] [2]

G. F. Chapline and N. S. Manton, Phys. Lett. B 120, 105 (1983)

work page 1983

[4] [3]

M. Dine, R. Rohm, N. Seiberg, and E. Witten, Phys. Lett. B 156, 55 (1985)

work page 1985

[5] [4]

Notably, since the formulas (

are relatively lengthy and involve a generous handful of Fierz identi- ties. Notably, since the formulas (

work page

[6] [5]

Kupka, C

J. Kupka, C. Strickland-Constable, and F. Valach, On higher fermions in supergravity (2024), arXiv:2412.04968 [hep-th]

arXiv 2024

[7] [6]

as they are not symmetries of the met- ric tensor formulation of the theory.) We postpone the details of the calculation to a future work [21]. BV FIELD SP ACE To construct the BV space we start with the classical ﬁeld space, add ghosts and ghosts for ghosts correspond- ing to local symmetries, and then adjoin the correspond- ing antiﬁelds. This yields th...

work page

[8] [7]

Coimbra, C

A. Coimbra, C. Strickland-Constable, and D. Waldram, JHEP 11, 091 , arXiv:1107.1733 [hep-th]

arXiv