Seifert fibering operators in 3d $$ \mathcal{N}=2 $$ theories

We study a perturbative expansion of the squashed 3-sphere (S 3 b ) partition function of 3d N = 2 gauge theories around the squashing parameter b = 1. Our proposal gives the coefficients of the perturbative expansion as a finite sum over the saddle points of the supersymmetric-localization integral in the limit b → 0 (the so-called Bethe vacua), and the contribution from each Bethe vacua can be systematically computed using saddle-point methods. Our expansion provides an efficient and practical method for computing basic CFT data (F, C T , C JJ and higher-point correlation functions of the stress-energy tensor) of the IR superconformal field theory without performing the localization integrals.1 There is no term linear in b − 1, as expected from the symmetry b → b −1 of the geometry (1.1). 2 There are counterexamples to the conjecture that CT decreases along the RG flow [11].

“…From the comparison between eq. (3.19) and the explicit expression for H α and F α given in [25], it is straightforward to check that…”

Section: Expansion At B → 1 (Convergent Expansion)mentioning

confidence: 99%

“…A careful treatment of these terms can be found e.g. in [22,25]. We will not keep track of them but instead will define the partition function Z b only up to an overall factor…”

Section: Localization On S 3 Bmentioning

confidence: 99%

Section: Expansion At B → 1 (Convergent Expansion)mentioning

confidence: 99%

Section: Expansion At B → 1 (Convergent Expansion)mentioning

confidence: 99%

See 2 more Smart Citations

Expanding 3d $$ \mathcal{N} $$ = 2 theories around the round sphere

Gang

Yamazaki

2020

“…One can also define an index for a topologically twisted theory on a circle fibered over a Riemann surface of genus g [60][61][62][63][64]. If g = 0, i.e., if the Riemann surface is a sphere, one can refine the index by turning on the angular momentum fugacity.…”

Section: The Refined Topologically Twisted Indexmentioning

confidence: 99%

Universal 3d Cardy block and black hole entropy

Choi

Hwang

2020

We discuss the Cardy limit of 3d supersymmetric partition functions which allow the factorization into the hemisphere indices: the generalized superconformal index, the refined topologically twisted index and the squashed sphere partition function. In the Cardy limit, the hemisphere index can be evaluated by the saddle point approximation where there exists a dominant saddle point contribution, which we call the Cardy block. The Cardy block turns out to be a simple but powerful object as it is a building block of other partition functions in the Cardy limit. The factorization to the Cardy block allows us to find universal relations among the partition functions, which we formulate as index theorems. Furthermore, if we consider a holographic 3d SCFT and its large N limit, those partition functions relate to various entropic quantities of the dual gravity theory in AdS 4 . As a result, our result provides the microscopic derivation of the universal relations among those entropic quantities of the gravity theory. We also discuss explicit examples, which confirm our general index theorems.

Rotating attractors and BPS black holes in AdS4

Hristov

Katmadas

Toldo

2019

144

We analyze stationary BPS black hole solutions to 4d N = 2 abelian gauged supergravity. Using an appropriate near horizon ansatz, we construct rotating attractors with magnetic flux realizing a topological twist along the horizon surface, for any theory with a symmetric scalar manifold. An analytic flow to asymptotically locally AdS 4 is presented for a subclass of these near-horizon geometries, and an explicit new example of supersymmetric AdS 4 rotating black hole is discussed in detail. We further note that, upon tuning the gauging to special values, one can obtain solutions with different asymptotics, and in particular reductions of doubly spinning asymptotically AdS 5 black holes. Finally we present a proposal for the form of the BPS entropy function with rotation, which we expect to be holographically related to the refined twisted index of the dual theory.