Gravity Dual of Two-Dimensional N=(2,2)∗\mathcal{N} = (2,2)^* Supersymmetric Yang-Mills Theory and Integrable Models

The 2D $\mathcal{N}=(2,2)^*$ supersymmetric Yang-Mills theory can be obtained from the 2D $\mathcal{N}=(4,4)$ theory with a twisted mass deformation. In this paper we construct the gravity dual theory of the 2D $\mathcal{N}=(2,2)^*$ supersymmetric $U(N)$ Yang-Mills theory at the large $N$ and large 't Hooft coupling limit using the 5D gauged supergravity. In the UV regime, this construction also provides the gravity dual of the 2D $\mathcal{N}=(2,2)^*$ $U(N)$ topological Yang-Mills-Higgs theory. We propose a triality in the UV regime among integrable model, gauge theory and gravity, and we make some checks of this relation at classical level.Comment: 49 pages, 3 figures; V2: typos corrected, more discussions adde

Note on Nonlinear Schr\"odinger Equation, KdV Equation and 2D Topological Yang-Mills-Higgs Theory

In this paper we discuss the relation between the (1+1)D nonlinear Schr\"odinger equation and the KdV equation. By applying the boson/vortex duality, we can map the classical nonlinear Schr\"odinger equation into the classical KdV equation in the small coupling limit, which corresponds to the UV regime of the theory. At quantum level, the two theories satisfy the Bethe Ansatz equations of the spin-$\frac{1}{2}$ XXX chain and the XXZ chain in the continuum limit respectively. Combining these relations with the dualities discussed previously in the literature, we propose a duality web in the UV regime among the nonlinear Schr\"odinger equation, the KdV equation and the 2D $\mathcal{N}=(2,2)^*$ topological Yang-Mills-Higgs theory.Comment: 20 pages, 1 figure; V2: typos correcte

Entanglement Entropy of ABJM Theory and Entropy of Topological Black Hole

In this paper we discuss the supersymmetric localization of the 4D $\mathcal{N}=2$ 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. It provides an explicit example of the identification of the entanglement entropy of the boundary conformal field theory with 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.Comment: 34 pages, 1 figure; minor changes in v2; references added in v3, published version in JHE

Thermal Corrections to Renyi Entropies for Conformal Field Theories

We compute thermal corrections to R\'enyi entropies of $d$ dimensional conformal field theories on spheres. Consider the $n$th R\'enyi entropy for a cap of opening angle $2 \theta$ on $S^{d-1}$. From a Boltzmann sum decomposition and the operator-state correspondence, the leading correction is related to a certain two-point correlation function of the operator (not equal to the identity) with smallest scaling dimension. More specifically, via a conformal map, the correction can be expressed in terms of the two-point function on a certain conical space with opening angle $2\pi n$. In the case of free conformal field theories, this two-point function can be computed explicitly using the method of images. We perform the computation for the conformally coupled scalar. From the $n \to 1$ limit of our results, we extract the leading thermal correction to the entanglement entropy, reproducing results of arXiv:1407.1358.Comment: 18 pages, 5 figures; v2 reference adde

Localization of Supersymmetric Chern-Simons-Matter Theory on a Squashed S3S^3 with SU(2)×U(1)SU(2)\times U(1) Isometry

Localization of supersymmetric $\mathcal{N}=2$ Chern-Simons-Matter theory on a squashed $S^3$ with $SU(2)\times U(1)$ isometry has been studied by different groups of authors. In this paper, we localize the theory on a squashed $S^3$ with $SU(2)\times U(1)$ isometry and a class of complex background. We see that certain kinds of shifts of the background gauge fields are crucial in obtaining nontrivial results, and the previously found results on this manifold can be incorporated in our results as special limits.Comment: 45 pages, Appendix D and some references added, typos correcte

Universal Entropy and Hawking Radiation of Near-Extremal AdS4_4 Black Holes

We compute the Bekenstein-Hawking entropy of near-extremal asymptotically AdS$_4$ electrically charged rotating black holes using three different methods: (i) from the gravity solution, (ii) from the near-horizon Kerr/CFT correspondence and (iii) from the boundary conformal field theory. The results from these three different approaches match exactly, giving us a unique and universal expression for the entropy and the microstate counting of near-extremal AdS black holes via the AdS/CFT correspondence. In the second method, we extend the Kerr/CFT correspondence to the near-extremal case to compute the left and right central charges. We also use hidden conformal symmetry of the near-horizon geometry to compute the Frolov-Thorne temperatures. From the results of the near-extremal AdS$_4$ black hole entropy, we provide a microscopic foundation for Hawking radiation.Comment: 25 pages, 2 figures; v2: Sec. 2.1 and Sec. 2.3 updated; v3: published version in JHEP, minor changes in Sec. 2 and