Localization of 4d $$ \mathcal{N} $$ = 1 theories on 𝔻2× 𝕋2

We study holomorphic blocks in the three dimensional N = 2 gauge theory that describes the CP 1 model. We apply exact WKB methods to analyze the line operator identities associated to the holomorphic blocks and derive the analytic continuation formulae of the blocks as the twisted mass and FI parameter are varied. The main technical result we utilize is the connection formula for the 1 φ 1 q-hypergeometric function. We show in detail how the q-Borel resummation methods reproduce the results obtained previously by using block-integral methods.

Section: Introductionmentioning

confidence: 99%

Exact WKB analysis of ℂℙ1 holomorphic blocks

Ashok

Subramanian

Bawane

et al. 2019

“…As discussed in section 9, such subtlety seems absent in our problem 117. For the computations of hemisphere partition functions (and the disk one-point functions) from localization, see[233][234][235][236][237].…”

mentioning

confidence: 99%

Structure constants in $$ \mathcal{N} $$ = 4 SYM at finite coupling as worldsheet g-function

Jiang

Komatsu

Vescovi

2020

173

We develop a novel nonperturbative approach to a class of three-point functions in planar N = 4 SYM based on Thermodynamic Bethe Ansatz (TBA). More specifically, we study three-point functions of a non-BPS single-trace operator and two determinant operators dual to maximal Giant Graviton D-branes in AdS 5 ×S 5. They correspond to disk one-point functions on the worldsheet and admit a simpler and more powerful integrability description than the standard single-trace three-point functions. We first introduce two new methods to efficiently compute such correlators at weak coupling; one based on large N collective fields, which provides an example of open-closed-open duality discussed by Gopakumar, and the other based on combinatorics. The results so obtained exhibit a simple determinant structure and indicate that the correlator can be interpreted as a generalization of g-functions in 2d QFT; an overlap between an integrable boundary state and a state corresponding to the single-trace operator. We then determine the boundary state at finite coupling using the symmetry, the crossing equation and the boundary Yang-Baxter equation. With the resulting boundary state, we derive the ground-state g-function based on TBA and conjecture its generalization to other states. This is the first fully nonperturbative proposal for the structure constants of operators of finite length. The results are tested extensively at weak and strong couplings. Finally, we point out that determinant operators can provide better probes of sub-AdS locality than single-trace operators and discuss possible applications.

“…It is interesting to know whether such factorization structure can survive in the one-loop level with the Spin Matrix theory coupling turned on and also what is the corresponding effect on the 2d elliptic genera. Also following the spirit of [37,42,43], which studied the SL(3, Z) modularity of 4d supersymmetric partition function, we can ask how the SL(3, Z) modularity can be affected considering the Spin Matrix theory is not protected by supersymmetry. The answers to these questions might shed light on the structures of 4d conformal field theories beyond supersymmetry.…”

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

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.