Cardy limits of 6d superconformal theories

Lee, Kimyeong; Nahmgoong, June

doi:10.1007/jhep05(2021)118

Cited by 16 publications

(25 citation statements)

References 62 publications

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“…Another possible extension of our approach is to 6d theories, which should similarly have a second sheet and a manifestly supersymmetric 5d effective theory describing the high-temperature expansion. See [28,[62][63][64] for some work on the subject, building on the method developed for the first sheet [20,65,66].…”

Section: Introductionmentioning

confidence: 99%

EFT and the SUSY index on the 2nd sheet

Komargodski

2021

SciPost Phys.

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The counting of BPS states in four-dimensional \mathcal{N}=1𝒩=1 theories has attracted a lot of attention in recent years. For superconformal theories, these states are in one-to-one correspondence with local operators in various short representations. The generating function for this counting problem has branch cuts and hence several Cardy-like limits, which are analogous to high-temperature limits. Particularly interesting is the second sheet, which has been shown to capture the microstates and phases of supersymmetric black holes in AdS_55. Here we present a 3d Effective Field Theory (EFT) approach to the high-temperature limit on the second sheet. We use the EFT to derive the behavior of the index at orders \beta^{-2},\beta^{-1},\beta^0β−2,β−1,β0. We also make a conjecture for O(\beta)O(β), where we argue that the expansion truncates up to exponentially small corrections. An important point is the existence of vector multiplet zero modes, unaccompanied by massless matter fields. The runaway of Affleck-Harvey-Witten is however avoided by a non-perturbative confinement mechanism. This confinement mechanism guarantees that our results are robust.

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Section: Introductionmentioning

confidence: 99%

EFT and the SUSY index on the 2nd sheet

Komargodski

2021

SciPost Phys.

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“…With all the ingredients we have, we can now perform a similar computation for the asymptotic entropy as was done in [79]. The result is…”

Section: Jhep07(2021)179mentioning

confidence: 96%

“…One can do a similar computation outside of the canonical chamber, but it needs modification on the asymptotic behavior of (5.12). For ADE-type theories, such computation was performed in [35,79], and the result restores the periodicity m ∼ m + 2πi. We expect that the Cardy formulas for twisted (2, 0) theories are also periodic under m ∼ m + 2πi.…”

Section: Jhep07(2021)179mentioning

confidence: 98%

“…Furthermore, Cardy formulas have been used to account the Bekenstein-Hawking entropy of supersymmetric black holes in various dimensions [77,78]. In the case of 6d, the Cardy formulas of (2, 0) ADE theories on R 4 ×T 2 were studied in [35,79]. The authors obtain the Cardy free energy by summing over the elliptic genera using continuum approximation and S-duality.…”

Section: D Twisted Theories In the Cardy Limitmentioning

confidence: 99%

“…In the computation above, the non-zero value of the saddle point (5.18) has a special importance. Physically, it indicates that the string charge n condensates to a non-zero expectation value in the Cardy limit [79]. From the saddle point of x in (5.18), the string charge n in (5.16) can be written as follows,…”

Section: Jhep07(2021)179mentioning

confidence: 99%

See 2 more Smart Citations

Twisted 6d (2, 0) SCFTs on a circle

Duan

Lee

Nahmgoong

et al. 2021

J. High Energ. Phys.

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We study twisted circle compactification of 6d (2, 0) SCFTs to 5d $$ \mathcal{N} $$ N = 2 supersymmetric gauge theories with non-simply-laced gauge groups. We provide two complementary approaches towards the BPS partition functions, reflecting the 5d and 6d point of view respectively. The first is based on the blowup equations for the instanton partition function, from which in particular we determine explicitly the one-instanton contribution for all simple Lie groups. The second is based on the modular bootstrap program, and we propose a novel modular ansatz for the twisted elliptic genera that transform under the congruence subgroups Γ0(N) of SL(2, ℤ). We conjecture a vanishing bound for the refined Gopakumar-Vafa invariants of the genus one fibered Calabi-Yau threefolds, upon which one can determine the twisted elliptic genera recursively. We use our results to obtain the 6d Cardy formulas and find universal behaviour for all simple Lie groups. In addition, the Cardy formulas remain invariant under the twist once the normalization of the compact circle is taken into account.

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Holomorphic anomalies, fourfolds and fluxes

Lee

Lerche

Lockhart

et al. 2022

J. High Energ. Phys.

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We investigate holomorphic anomalies of partition functions underlying string compactifications on Calabi-Yau fourfolds with background fluxes. For elliptic fourfolds the partition functions have an alternative interpretation as elliptic genera of N = 1 supersymmetric string theories in four dimensions, or as generating functions for relative, genus zero Gromov-Witten invariants of fourfolds with fluxes. We derive the holomorphic anomaly equations by starting from the BCOV formalism of topological strings, and translating them into geometrical terms. The result can be recast into modular and elliptic anomaly equations. As a new feature, as compared to threefolds, we find an extra contribution which is given by a gravitational descendant invariant. This leads to linear terms in the anomaly equations, which support an algebra of derivatives mapping between partition functions of the various flux sectors. These geometric features are mirrored by certain properties of quasi-Jacobi forms. We also offer an interpretation of the physics from the viewpoint of the worldsheet theory, and comment on holomorphic anomalies at genus one.

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Cardy limits of 6d superconformal theories

Cited by 16 publications

References 62 publications

EFT and the SUSY index on the 2nd sheet

EFT and the SUSY index on the 2nd sheet

Twisted 6d (2, 0) SCFTs on a circle

Holomorphic anomalies, fourfolds and fluxes

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