Xinyu Zhang

Type

Text

Type

Dissertation

Advisor

Nekrasov, Nikita. | Nekrasov, Nikita | Rocek, Martin | Du, Xu | Takhtajan, Leon.

Date

2017-08-01

Keywords

Theoretical physics

Department

Department of Physics.

Language

en_US

Source

This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree

Identifier

http://hdl.handle.net/11401/78114

Publisher

The Graduate School, Stony Brook University: Stony Brook, NY.

Format

application/pdf

Abstract

This thesis is devoted to a number of exact computations in various supersymmetric quantum field theories and their applications in studying non-perturbative properties of the theories. In the first part, we study four-dimensional $\CN=2$ supersymmetric theory on the $\Omega$-background. We show that the partition function of $U(N)$ gauge theory with $2N$ fundamental hypermultiplets on the self-dual $\Omega$-background simplifies at special points of the parameter space, and is related to the partition function of two-dimensional Yang-Mills theory on $S^2$. We also consider the insertion of a Wilson loop operator in two-dimensional Yang-Mills theory, and find the corresponding operator in the four-dimensional theory. In the second part, we analyze the dynamics of a general two-dimensional $\CN=(2,2)$ gauged linear sigma model with semichiral superfields. By computing the elliptic genera, we study the vacuum structure of the model. The result coincides with the model without the semichiral superfields. We also show that the low energy effective twisted superpotential contributed by semichiral superfields vanishes, whether we turn on twisted masses or not. In the third part, we discuss the supersymmetric localization of the four-dimensional $\mathcal{N}=2$ off-shell gauged supergravity in the background of the $\textrm{AdS}_4$ neutral topological black hole, which is the gravity dual of the ABJM theory defined on the boundary $\textrm{S}^1 \times \mathbb{H}^2$. We compute the large-$N$ expansion of the supergravity partition function. The result gives the black hole entropy with the logarithmic correction, which matches the previous result of the entanglement entropy of the ABJM theory up to some stringy effects. Our result is consistent with the previous on-shell one-loop computation of the logarithmic correction to black hole entropy, and it provides a concrete example for the identification of the entanglement entropy of the boundary conformal field theory and the bulk black hole entropy beyond the leading order given by the classical Bekenstein-Hawking formula, which consequently tests the AdS/CFT correspondence at the subleading order. | 105 pages

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