3-charge geometries and their CFT duals

Ashish Saxena; Samir D. Mathur; Stefano Giusto

REVIEW

3-charge geometries and their CFT duals

Stefano Giusto, Samir D. Mathur, Ashish Saxena

High Energy Physics - Theory · Submitted 11 Jun 2004 · 31 references

Pith's verdict: The geometry side is solid and checkable; the CFT state identification for the S,T-dual family is the soft spot, and the authors say so themselves in §6.3.

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arXiv IDhep-th/0406103 (version 2)

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CitationAshish Saxena, Samir D. Mathur, Stefano Giusto. "3-charge geometries and their CFT duals." arXiv:hep-th/0406103 (2004). https://pith.science/paper/YZ7IXXQ3

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Significance

If correct, the paper substantially widens the class of three-charge microstates for which an explicit horizonless, CTC-free supergravity dual is known, and thereby strengthens the fuzzball picture beyond the special k = 1 case of [6]. The geometry checks in Appendix B are explicit and reproducible, and the wave-equation analysis in Appendices D and E is careful: the matching across the inner and outer regions is done in a controlled low-frequency limit, and the resulting travel time and absorption probability are stated in closed form. The observation that m and T̂ are invariant under S,T duality is a genuinely nontrivial structural result, and the threshold computation in §6.2 provides an independent, non-circular check on the state identification: the wave-equation threshold (6.21) is derived from the geometry, not assumed from the CFT. The paper is also candid about what it has not shown, which is a strength.

Major objections (1)

[§6.3, with §6.1.3] The title and §1 promise the CFT duals of both families, but the dual of the S,T-dualized family (3.2) is identified only conjecturally with the state (6.18). The authors themselves note in §6.3 that (6.18) assigns fractional momentum to each component string, which the orbifold CFT forbids, and the two proposed resolutions (a deformation away from the orbifold point, or an iterated orbifold) are not constructed. The evidence offered, namely the travel time (6.8) and the absorption threshold (6.21), is substantial and, I agree with the authors, is not circular, since the threshold is an independent wave-equation computation. But it establishes that (6.18) is the natural candidate, not that it is the dual. I recommend that the abstract and §1 state explicitly that the identification for family (b) is conjectural, and that §6.3 say what observation would confirm or refute it. The geometry claims (no horizon, no CTC) are unaffected, since S,T duality guarantees that some dual state exists.

Minor objections (7)

[Abstract and §1] The abstract says the geometries 'cap off smoothly near r = 0', but §4.2 establishes orbifold singularities for k > 1 in family (a) and along two curves in family (b), and §1 itself says 'most will have an orbifold singularity along certain curves'. The word 'smoothly' should be replaced by 'without horizons', or the orbifold caveat should be added to the abstract.
[Eq. (A.3)] The D5 charge is written as Q5 = (M/2) sinh 2δp; it should be sinh 2δ5, since Qp is the quantity defined with δp.
[§6.2.2, final paragraph] The statement that 'the absorption computation applies equally to both sets of geometries' is asserted rather than shown. Since (3.2) is stated in §3 to be of the general form (2.46) with the parameter map (3.4), the carry-over is straightforward, but the paper should say explicitly that substituting (3.4) into (5.5)-(5.7) gives the threshold for (3.2), and should track the primed η' in the travel time (6.8).
[§5.2.4] The claim that the factor η makes Δt in (5.33) invariant under the D1/D5/P permutations is asserted rather than demonstrated. The redshift interpretation via (5.37)-(5.38) is convincing for the η factor itself, but the invariance of the full combination πR/(ηγ) requires the transformation of R under the duality chain, which is not shown. Either display that transformation or cite footnote 3 explicitly at this point.
[§2.1.4] The identification of (2.27) with the spectral flow of (2.8) at n = 1 requires the flow to be applied per component string with effective central charge 6k, not to the full c = 6N theory; applying (2.11)-(2.12) with c = 6N to (2.8) gives h = N(5/4 - k), which is negative for k ≥ 2. The paper should state this convention explicitly, since (2.11)-(2.12) are written generically.
[§4.2.2] The derivation of the orbifold action (4.15) and of the fixed-point orders kn + 1 and mn is dense. A short explicit check, for example that ω^{n5 n} shifts ỹ by 2π/(kn + 1) and acts trivially on ψ̃, would make the argument much easier to verify.
[§5.1] The regime of validity of the supergravity approximation is not discussed. Since the cap size is of order (Q1Q5)^{1/4}, the reader would benefit from an explicit statement that this is large compared with the string scale in the classical limit, so that the smooth-cap conclusion is not an artifact of a string-scale geometry.

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The paper

The paper claims

The paper constructs gravity duals for two families of three-charge D1-D5-P states and argues that each geometry caps off near the origin, with no horizon and no closed timelike curves.

The reading

The paper asks whether the interior of an extremal three-charge black hole really contains a horizon and a singularity, or whether each microstate is instead a horizonless 'fuzzball' geometry that ends smoothly. It builds two families of D1-D5-P geometries: one by spectral flow from known two-charge D1-D5 solutions, and one by S,T dualities that exchange the D1 and momentum charges. In both families the throat closes off near $r=0$, leaving only orbifold singularities along curves, and the authors check that the metrics have no horizons or closed timelike curves. They then identify the dual CFT states by matching the round-trip travel time of a scalar and the absorption threshold to the excitation spectrum of effective strings. The result extends earlier three-charge examples and supports the broader claim that black-hole interiors are nontrivial all the way to the horizon.

What carries the argument

The load-bearing machinery is the correspondence between the length of a component string in the CFT and the round-trip travel time of a quantum down the gravity throat. Spectral flow turns a two-charge D1-D5 state into a three-charge D1-D5-P state; $S,T$ dualities then permute the charges. The conical defect angle $2π(1-1/k)$ identifies the orbifold action and the winding number $k$, while the absorption threshold $β>α+ν+1/2$ identifies which CFT levels are occupied. Matching these quantities fixes the dual state and shows that $m=N/k$ is duality invariant.

Extended reading notes

Core claim

The central claim is that two explicit families of BPS D1-D5-P states have capped, horizonless gravity duals. The first family comes from spectral flow of the two-charge D1-D5 geometries labelled by $0<γ≤1$; for $γ=1/k$ the resulting three-charge metrics have a $Z_k$ orbifold singularity but no horizon. The second family is obtained by an $S,T$-duality chain that swaps the D1 and momentum charges; these metrics have two nonintersecting orbifold $S^1$ curves, of orders $kn+1$ and $mn$. In both cases the geometry caps off at $r=0$, and the authors verify that the determinant of the metric restricted to the periodic coordinates has no extra zeros, so there are no closed timelike curves. They identify the CFT duals by computing the scalar travel time $Δ t=πR/(ηγ)$ and the absorption threshold, finding that the number of component strings $m$ is unchanged under the duality even though the individual winding number $k$ changes.

Load-bearing premise

The weakest premise is that the $S,T$-dualized geometry is dual to the CFT state of Eq. (6.18), with equal-winding component strings, even though the momentum per component string is fractional and the orbifold CFT requires integral momentum; the authors acknowledge this in §6.3 and leave a deformation or iterated orbifold unresolved.

Editorial extensions

If this is right

If correct, every state in these families is horizonless, so the naive black-hole horizon is not part of the microstate geometry.
The component-string count $m$ is invariant under $S,T$ duality, giving a duality-invariant way to count independent effective strings.
The travel-time and threshold matching gives a practical dictionary between bulk wave dynamics and CFT level occupations for three-charge states.
The orbifold singularities are interpreted as limits of smooth geometries rather than as physical singularities.
The result motivates looking beyond the orbifold CFT because fractional momentum per component string appears.

Reading between the lines

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

The fractional-momentum puzzle suggests that the orbifold point is not the right description for all D1-D5-P states; a deformation or an iterated orbifold may be needed.
If the same capping mechanism works for non-extremal or near-extremal holes, the horizon might emerge only after coarse-graining over microstates.
The duality-invariant count $m$ could serve as a coarse observable for counting microstates, perhaps connecting to black-hole entropy.
The two orbifold curves in the $S,T$-dual family may signal a more general 'spacetime bit' structure in which each duality frame exposes different defects.

Original abstract

We consider two families of D1-D5-P states and find their gravity duals. In each case the geometries are found to `cap off' smoothly near r=0; thus there are no horizons or closed timelike curves. These constructions support the general conjecture that the interior of black holes is nontrivial all the way up to the horizon.

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.17 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.17 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

We consider two families of D1-D5-P states and find their gravity duals. In each case the geometries are found to `cap off' smoothly near r=0; thus there are no horizons or closed timelike curves. These constructions support the general conjecture that the interior of black holes is nontrivial all the way up to the horizon.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We consider two families of D1-D5-P states and find their gravity duals.	contribution 1.00	0.95	0.09	asserted 1.00
s1	In each case the geometries are found to `cap off' smoothly near r=0; thus there are no horizons or closed timelike curves.	result 1.00	0.94	0.24	asserted 1.00
s2	These constructions support the general conjecture that the interior of black holes is nontrivial all the way up to the horizon.	interpretation 1.00	0.28	0.67	hedged possibility 0.53

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.98.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 1.** (a) Naive geometry of 3-charge D1-D5-P; there is a horizon at r = 0 and a singularity past the horizon. (b) Expected geometries for D1-D5-P; the area at the dashed line will give A 4G = 2π √n1n5np. 2

Figures reproduced from arXiv:hep-th/0406103 by the authors.

References

Works cited (31)

[6]

S. Giusto, S. D. Mathur and A. Saxena, arXiv:hep-th/0405017

View on Pith Pith review arXiv
[1]

S. W. Hawking, Commun. Math. Phys. 43, 199 (1975)

View on Pith 1975
[2]

S. D. Mathur, Nucl. Phys. B 529, 295 (1998) [arXiv:hep-th/9706151]

View on Pith Pith review arXiv 1998
[3]

O. Lunin and S. D. Mathur, Nucl. Phys. B 623, 342 (2002) [arXiv:hep-th/0109154]

View on Pith Pith review arXiv 2002
[4]

O. Lunin, JHEP 0404, 054 (2004) [arXiv:hep-th/0404006]

View on Pith Pith review arXiv 2004
[5]

S. D. Mathur, A. Saxena and Y. K. Srivastava, Nucl. Phys. B 680, 415 (2004) [arXiv:hep-th/0311092]

View on Pith Pith review arXiv 2004
[7]

D. Mateos and P. K. Townsend, Phys. Rev. Lett. 87, 011602 (2001) [arXiv:hep-th/0103030]; R. Emparan, D. Mateos and P. K. Townsen d, JHEP 0107, 011 (2001) [arXiv:hep-th/0106012]

View on Pith Pith review arXiv 2001
[8]

I. Bena and P. Kraus, arXiv:hep-th/0402144

View on Pith Pith review arXiv
[9]

I. Bena, arXiv:hep-th/0404073

View on Pith Pith review arXiv
[10]

B. C. Palmer and D. Marolf, arXiv:hep-th/0403025

View on Pith Pith review arXiv
[11]

V. Balasubramanian, J. de Boer, E. Keski-Vakkuri and S. F. Ro ss, Phys. Rev. D 64, 064011 (2001) [arXiv:hep-th/0011217]

View on Pith Pith review arXiv 2001
[12]

J. M. Maldacena and L. Maoz, JHEP 0212, 055 (2002) [arXiv:hep-th/0012025]

View on Pith Pith review arXiv 2002
[13]

M. Cvetic and D. Youm, Nucl. Phys. B 476, 118 (1996) [arXiv:hep-th/9603100]; D. Youm, Phys. Rept. 316, 1 (1999) [arXiv:hep-th/9710046]; M. Cvetic and F. Larsen, Nucl. Phys. B 531, 239 (1998) [arXiv:hep-th/9805097]

View on Pith Pith review arXiv 1996
[14]

N. Seiberg and E. Witten, JHEP 9904, 017 (1999) [arXiv:hep-th/9903224]; F. Larsen and E. J. Martinec, JHEP 9906, 019 (1999) [arXiv:hep-th/9905064]; J. de Boer, Nucl. Phys. B 548, 139 (1999) [arXiv:hep-th/9806104]

View on Pith Pith review arXiv 1999
[15]

O. Lunin and S. D. Mathur, Commun. Math. Phys. 219, 399 (2001) [arXiv:hep-th/0006196]

View on Pith Pith review arXiv 2001
[16]

O. Lunin and S. D. Mathur, Commun. Math. Phys. 227, 385 (2002) [arXiv:hep-th/0103169]

View on Pith Pith review arXiv 2002
[17]

A. Schwimmer and N. Seiberg, Phys. Lett. B 184, 191 (1987). 41

View on Pith 1987
[18]

O. Lunin, J. Maldacena and L. Maoz, arXiv:hep-th/0212210

View on Pith Pith review arXiv
[19]

C. A. R. Herdeiro, Nucl. Phys. B 582, 363 (2000) [arXiv:hep-th/0003063]; C. A. R. Herdeiro, Nucl. Phys. B 665, 189 (2003) [arXiv:hep-th/0212002]; L. Dyson, JHEP 0403, 024 (2004) [arXiv:hep-th/0302052]; N. Drukker, arXiv:hep-th/0 404239; E. G. Gimon and P. Horava, arXiv:hep-th/0405019

View on Pith Pith review arXiv 2000
[20]

I. Y. Park, arXiv:hep-th/0403218

View on Pith Pith review arXiv
[21]

M. Cvetic and F. Larsen, Phys. Rev. D 56, 4994 (1997) [arXiv:hep-th/9705192]

View on Pith Pith review arXiv 1997
[22]

O. Lunin and S. D. Mathur, Nucl. Phys. B 615, 285 (2001) [arXiv:hep-th/0107113]

View on Pith Pith review arXiv 2001
[23]

O. Lunin and S. D. Mathur, Nucl. Phys. B 642, 91 (2002) [arXiv:hep-th/0206107]

View on Pith Pith review arXiv 2002
[24]

C. G. Callan and J. M. Maldacena, Nucl. Phys. B 472, 591 (1996) hep-th/9602043

View on Pith Pith review arXiv 1996
[25]

S. R. Das and S. D. Mathur, Nucl. Phys. B 478, 561 (1996) [arXiv:hep-th/9606185]

View on Pith Pith review arXiv 1996
[26]

S. D. Mathur, Nucl. Phys. B 514, 204 (1998) [arXiv:hep-th/9704156]; S. S. Gub- ser, Phys. Rev. D 56, 4984 (1997) [arXiv:hep-th/9704195]; J. M. Maldacena and A. Strominger, Phys. Rev. D 56, 4975 (1997) [arXiv:hep-th/9702015]

View on Pith Pith review arXiv 1998
[27]

F. Larsen and E. J. Martinec, JHEP 9906, 019 (1999) [arXiv:hep-th/9905064]

View on Pith Pith review arXiv 1999
[28]

J. Gomis, L. Motl and A. Strominger, JHEP 0211, 016 (2002) [arXiv:hep-th/0206166]

View on Pith Pith review arXiv 2002
[29]

S. Gukov, E. Martinec, G. Moore and A. Strominger, arXiv:hep- th/0404023

View on Pith
[30]

R. Dijkgraaf, Nucl. Phys. B 543, 545 (1999) [arXiv:hep-th/9810210]

View on Pith Pith review arXiv 1999
[31]

J. C. Breckenridge, R. C. Myers, A. W. Peet and C. Vafa, Phys . Lett. B 391, 93 (1997) [arXiv:hep-th/9602065]. 42

View on Pith Pith review arXiv 1997

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How the literature uses it

72 arXiv papers cite this in 154 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 · 100 sentences without a confident label

Contests it 1 paper

As far as we know, such a construction doesn't exist yet and the microscopic solutions constructed in the fuzzball program [ref] so far face the issue we discussed in Sec. [ref] as they don't satisfy the definition Equ.

Microscopic Origin of the Entropy of Single-sided Black Holes · Conclusions and Discussions · contest 0.73

Builds on it 2 papers

Here we will extend that analysis to the more general geometries of [ref] ; the reader can refer to [ref] for more details of the CFT construction.

Radiation from the non-extremal fuzzball · The states we consider · 0.99
This separability of the Hamilton-Jacobi equation is due to the fact that these spacetimes have a 'hidden' symmetry related to a conformal Killing tensor which also allows the wave equation to separate in both cases [ref] .

Geodesics in supersymmetric microstate geometries · Introduction · 0.93

Uses its method or tool 1 paper

[ref] ) into the Hamilton-Jacobi equation [ref] we obtain first order equations for $R(r)$ and $Θ(θ)$.

Geodesics in supersymmetric microstate geometries · Equations of motion · 0.92

Compares with it 7 papers

If we set $m=n+1$, this metric should reduce to the familiar two-center supersymmetric solution of [ref] .

Geometry of non-supersymmetric three-charge bound states · Relation to the supersymmetric case · 0.98
This gap is found to agree exactly with the gap in the dual CFT state [ref] .

Radiation from the non-extremal fuzzball · Extremal holes · 0.85
The expression for the emission rate obtained above matches the one obtained in [ref] where it is given in a slightly different form.

Using the D1D5 CFT to Understand Black Holes · The Rate of Emission · 1.00

Cites it as support 1 paper

As shown in [ref] , the upper bound on the time scale is reproduced precisely in the fuzzball picture.

Microstate Dependence of Scattering from the D1-D5 System · Introduction and Summary · 0.96

Cites it as background 32 papers

In [ref] non-extremal geometries were constructed, with regularity properties similar to those of the extremal geometries in [ref] .

Radiation from the non-extremal fuzzball · Introduction · 0.88
The 2-charge extremal hole has been quite thoroughly understood [ref] , and there are a large class of states known for the 3-charge and 4-charge extremal holes [ref] .

Non-extremal fuzzballs and ergoregion emission · Introduction · 0.92
In this section we first review the three-charge, 1/8-BPS, fractionally spectral flowed supertube solutions constructed and studied in [ref] , as well as their decomposition into two-center solutions of the multi-center formalism of [ref] .

Shockwaves in black hole microstate geometries · Shockwaves in fractionally spectral flowed supertubes · 0.95

Discussion

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[1] [6]

S. Giusto, S. D. Mathur and A. Saxena, arXiv:hep-th/0405017

View on Pith Pith review arXiv

[2] [1]

S. W. Hawking, Commun. Math. Phys. 43, 199 (1975)

View on Pith 1975

[3] [2]

S. D. Mathur, Nucl. Phys. B 529, 295 (1998) [arXiv:hep-th/9706151]

View on Pith Pith review arXiv 1998

[4] [3]

O. Lunin and S. D. Mathur, Nucl. Phys. B 623, 342 (2002) [arXiv:hep-th/0109154]

View on Pith Pith review arXiv 2002

[5] [4]

O. Lunin, JHEP 0404, 054 (2004) [arXiv:hep-th/0404006]

View on Pith Pith review arXiv 2004

[6] [5]

S. D. Mathur, A. Saxena and Y. K. Srivastava, Nucl. Phys. B 680, 415 (2004) [arXiv:hep-th/0311092]

View on Pith Pith review arXiv 2004

[7] [7]

D. Mateos and P. K. Townsend, Phys. Rev. Lett. 87, 011602 (2001) [arXiv:hep-th/0103030]; R. Emparan, D. Mateos and P. K. Townsen d, JHEP 0107, 011 (2001) [arXiv:hep-th/0106012]

View on Pith Pith review arXiv 2001

[8] [8]

I. Bena and P. Kraus, arXiv:hep-th/0402144

View on Pith Pith review arXiv

[9] [9]

I. Bena, arXiv:hep-th/0404073

View on Pith Pith review arXiv

[10] [10]

B. C. Palmer and D. Marolf, arXiv:hep-th/0403025

View on Pith Pith review arXiv

[11] [11]

V. Balasubramanian, J. de Boer, E. Keski-Vakkuri and S. F. Ro ss, Phys. Rev. D 64, 064011 (2001) [arXiv:hep-th/0011217]

View on Pith Pith review arXiv 2001

[12] [12]

J. M. Maldacena and L. Maoz, JHEP 0212, 055 (2002) [arXiv:hep-th/0012025]

View on Pith Pith review arXiv 2002

[13] [13]

M. Cvetic and D. Youm, Nucl. Phys. B 476, 118 (1996) [arXiv:hep-th/9603100]; D. Youm, Phys. Rept. 316, 1 (1999) [arXiv:hep-th/9710046]; M. Cvetic and F. Larsen, Nucl. Phys. B 531, 239 (1998) [arXiv:hep-th/9805097]

View on Pith Pith review arXiv 1996

[14] [14]

N. Seiberg and E. Witten, JHEP 9904, 017 (1999) [arXiv:hep-th/9903224]; F. Larsen and E. J. Martinec, JHEP 9906, 019 (1999) [arXiv:hep-th/9905064]; J. de Boer, Nucl. Phys. B 548, 139 (1999) [arXiv:hep-th/9806104]

View on Pith Pith review arXiv 1999

[15] [15]

O. Lunin and S. D. Mathur, Commun. Math. Phys. 219, 399 (2001) [arXiv:hep-th/0006196]

View on Pith Pith review arXiv 2001

[16] [16]

O. Lunin and S. D. Mathur, Commun. Math. Phys. 227, 385 (2002) [arXiv:hep-th/0103169]

View on Pith Pith review arXiv 2002

[17] [17]

A. Schwimmer and N. Seiberg, Phys. Lett. B 184, 191 (1987). 41

View on Pith 1987

[18] [18]

O. Lunin, J. Maldacena and L. Maoz, arXiv:hep-th/0212210

View on Pith Pith review arXiv

[19] [19]

C. A. R. Herdeiro, Nucl. Phys. B 582, 363 (2000) [arXiv:hep-th/0003063]; C. A. R. Herdeiro, Nucl. Phys. B 665, 189 (2003) [arXiv:hep-th/0212002]; L. Dyson, JHEP 0403, 024 (2004) [arXiv:hep-th/0302052]; N. Drukker, arXiv:hep-th/0 404239; E. G. Gimon and P. Horava, arXiv:hep-th/0405019

View on Pith Pith review arXiv 2000

[20] [20]

I. Y. Park, arXiv:hep-th/0403218

View on Pith Pith review arXiv

[21] [21]

M. Cvetic and F. Larsen, Phys. Rev. D 56, 4994 (1997) [arXiv:hep-th/9705192]

View on Pith Pith review arXiv 1997

[22] [22]

O. Lunin and S. D. Mathur, Nucl. Phys. B 615, 285 (2001) [arXiv:hep-th/0107113]

View on Pith Pith review arXiv 2001

[23] [23]

O. Lunin and S. D. Mathur, Nucl. Phys. B 642, 91 (2002) [arXiv:hep-th/0206107]

View on Pith Pith review arXiv 2002

[24] [24]

C. G. Callan and J. M. Maldacena, Nucl. Phys. B 472, 591 (1996) hep-th/9602043

View on Pith Pith review arXiv 1996

[25] [25]

S. R. Das and S. D. Mathur, Nucl. Phys. B 478, 561 (1996) [arXiv:hep-th/9606185]

View on Pith Pith review arXiv 1996

[26] [26]

S. D. Mathur, Nucl. Phys. B 514, 204 (1998) [arXiv:hep-th/9704156]; S. S. Gub- ser, Phys. Rev. D 56, 4984 (1997) [arXiv:hep-th/9704195]; J. M. Maldacena and A. Strominger, Phys. Rev. D 56, 4975 (1997) [arXiv:hep-th/9702015]

View on Pith Pith review arXiv 1998

[27] [27]

F. Larsen and E. J. Martinec, JHEP 9906, 019 (1999) [arXiv:hep-th/9905064]

View on Pith Pith review arXiv 1999

[28] [28]

J. Gomis, L. Motl and A. Strominger, JHEP 0211, 016 (2002) [arXiv:hep-th/0206166]

View on Pith Pith review arXiv 2002

[29] [29]

S. Gukov, E. Martinec, G. Moore and A. Strominger, arXiv:hep- th/0404023

View on Pith

[30] [30]

R. Dijkgraaf, Nucl. Phys. B 543, 545 (1999) [arXiv:hep-th/9810210]

View on Pith Pith review arXiv 1999

[31] [31]

J. C. Breckenridge, R. C. Myers, A. W. Peet and C. Vafa, Phys . Lett. B 391, 93 (1997) [arXiv:hep-th/9602065]. 42

View on Pith Pith review arXiv 1997