Elliptic genus derivation of 4d holomorphic blocks

Poggi, Matteo

doi:10.1007/jhep03(2018)035

Cited by 7 publications

(6 citation statements)

References 29 publications

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“…It is also possible to compute this partition function from the point of view of the vortex worldsheet theory (see [43,44] for examples of such a computation in N = 1, 2 gauge theories). In particular, it should match the elliptic genus of a specific (4, 4) GLSM appearing for example in section 5.1 of [45].…”

Section: Jhep04(2021)216mentioning

confidence: 99%

Residues, modularity, and the Cardy limit of the 4d $$ \mathcal{N} $$ = 4 superconformal index

Goldstein

Jejjala

Lei

et al. 2021

J. High Energ. Phys.

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We compute the superconformal index of the $$ \mathcal{N} $$ N = 4 SU(N) Yang-Mills theory through a residue calculation. The method is similar in spirit to the Bethe Ansatz formalism, except that all poles are explicitly known, and we do not require specialization of any of the chemical potentials. Our expression for the index allows us to revisit the Cardy limit using modular properties of four-dimensional supersymmetric partition functions. We find that all residues contribute at leading order in the Cardy limit. In a specific region of flavour chemical potential space, close to the two unrefined points, in fact all residues contribute universally. These universal residues precisely agree with the entropy functions of the asymptotically AdS5 black hole and its “twin saddle” respectively. Finally, we discuss how our formula is suited to study the implications of four-dimensional modularity for the index beyond the Cardy limit.

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Section: Jhep04(2021)216mentioning

confidence: 99%

Residues, modularity, and the Cardy limit of the 4d $$ \mathcal{N} $$ = 4 superconformal index

Goldstein

Jejjala

Lei

et al. 2021

J. High Energ. Phys.

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show abstract

“…The free limit of partition function in 4d SCFT can be factorized into holomorphic blocks, which are the partition functions in D 2 × T 2 [36,37]. The blocks have been shown to be related to 2d elliptic genera [38,39] of the corresponding worldsheet theory. The geometric picture is that one can acquire the M 4 manifold by glueing two solid T 3 torus by an SL(3, Z) group element.…”

Section: Discussionmentioning

confidence: 99%

Symmetry structure of the interactions in near-BPS corners of $ \mathcal{N} = 4$ super-Yang-Mills

Baiguera,

Harmark,

Lei

et al. 2020

Preprint

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We consider limits of N = 4 super-Yang-Mills (SYM) theory that approach BPS bounds. These limits result in non-relativistic near-BPS theories that describe the effective dynamics near the BPS bounds and upon quantization are known as Spin Matrix theories. The near-BPS theories can be obtained by reducing N = 4 SYM on a three-sphere and integrating out the fields that become non-dynamical in the limits. We perform the sphere reduction for the near-BPS limit with SU(1, 2|2) symmetry, which has several new features compared to the previously considered cases with SU(1, 1) symmetry, including a dynamical gauge field. We discover a new structure in the classical limit of the interaction term. We show that the interaction term is built from certain blocks that comprise an irreducible representation of the SU(1, 2|2) algebra. Moreover, the full interaction term can be interpreted as a norm in the linear space of this representation, explaining its features including the positive definiteness. This means one can think of the interaction term as a distance squared from saturating the BPS bound. The SU(1, 1|1) near-BPS theory, and its subcases, is seen to inherit these features. These observations point to a way to solve the strong coupling dynamics of these near-BPS theories.

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“…The free limit of partition function in 4d SCFT can be factorized into holomorphic blocks, which are the partition functions in D 2 × T 2 [36,37]. The blocks have been shown to be related to 2d elliptic genera [38][39][40] of the corresponding worldsheet theory. The geometric picture is that one can acquire the M 4 manifold by glueing two solid T 3 torus by an SL(3, Z) group element.…”

Section: Jhep04(2021)029mentioning

confidence: 99%

Symmetry structure of the interactions in near-BPS corners of $$ \mathcal{N} $$ = 4 super-Yang-Mills

Baiguera

Harmark

Lei

et al. 2021

J. High Energ. Phys.

View full text Add to dashboard Cite

We consider limits of $$ \mathcal{N} $$ N = 4 super-Yang-Mills (SYM) theory that approach BPS bounds. These limits result in non-relativistic near-BPS theories that describe the effective dynamics near the BPS bounds and upon quantization are known as Spin Matrix theories. The near-BPS theories can be obtained by reducing $$ \mathcal{N} $$ N = 4 SYM on a three-sphere and integrating out the fields that become non-dynamical in the limits. We perform the sphere reduction for the near-BPS limit with SU(1, 2|2) symmetry, which has several new features compared to the previously considered cases with SU(1) symmetry, including a dynamical gauge field. We discover a new structure in the classical limit of the interaction term. We show that the interaction term is built from certain blocks that comprise an irreducible representation of the SU(1, 2|2) algebra. Moreover, the full interaction term can be interpreted as a norm in the linear space of this representation, explaining its features including the positive definiteness. This means one can think of the interaction term as a distance squared from saturating the BPS bound. The SU(1, 1|1) near-BPS theory, and its subcases, is seen to inherit these features. These observations point to a way to solve the strong coupling dynamics of these near-BPS theories.

show abstract

Elliptic genus derivation of 4d holomorphic blocks

Cited by 7 publications

References 29 publications

Residues, modularity, and the Cardy limit of the 4d $$ \mathcal{N} $$ = 4 superconformal index

Residues, modularity, and the Cardy limit of the 4d $$ \mathcal{N} $$ = 4 superconformal index

Symmetry structure of the interactions in near-BPS corners of $ \mathcal{N} = 4$ super-Yang-Mills

Symmetry structure of the interactions in near-BPS corners of $$ \mathcal{N} $$ = 4 super-Yang-Mills

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