arXiv subjects

Junya Yagi

Publications and source records attributed to Junya Yagi.

28 records · Page 2Linked to original sources

arXiv2016

Quiver gauge theories and integrable lattice models

We discuss connections between certain classes of supersymmetric quiver gauge theories and integrable lattice models from the point of view of topological quantum field theories (TQFTs). The relevant classes include 4d $\mathcal{N} = 1$ theories known as brane box and brane tilling models, 3d $\mathcal{N} = 2$ and 2d $\mathcal{N} = (2,2)$ theories obtained from them by compactification, and 2d $\mathcal{N} = (0,2)$ theories closely related to these theories. We argue that their supersymmetric indices carry structures of TQFTs equipped with line operators, and as a consequence, are equal to the partition functions of lattice models. The integrability of these models follows from the existence of extra dimension in the TQFTs, which emerges after the theories are embedded in M-theory. The Yang-Baxter equation expresses the invariance of supersymmetric indices under Seiberg duality and its lower-dimensional analogs.

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arXiv2015

Ω-deformation of B-twisted gauge theories and the 3d-3d correspondence

We study Ω-deformation of B-twisted gauge theories in two dimensions. As an application, we construct an Ω-deformed, topologically twisted five-dimensional maximally supersymmetric Yang-Mills theory on the product of a Riemann surface $Σ$ and a three-manifold $M$, and show that when $Σ$ is a disk, this theory is equivalent to analytically continued Chern-Simons theory on $M$. Based on these results, we establish a correspondence between three-dimensional $\mathcal{N} = 2$ superconformal theories and analytically continued Chern-Simons theory. Furthermore, we argue that there is a mirror symmetry between Ω-deformed two-dimensional theories.

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arXiv2014

Ω-deformation and quantization

We formulate a deformation of Rozansky-Witten theory analogous to the $Ω$-deformation. It is applicable when the target space $X$ is hyperkähler and the spacetime is of the form $\mathbb{R} \times Σ$, with $Σ$ being a Riemann surface. In the case that $Σ$ is a disk, the $Ω$-deformed Rozansky-Witten theory quantizes a symplectic submanifold of $X$, thereby providing a new perspective on quantization. As applications, we elucidate two phenomena in four-dimensional gauge theory from this point of view. One is a correspondence between the $Ω$-deformation and quantization of integrable systems. The other concerns supersymmetric loop operators and quantization of the algebra of holomorphic functions on a hyperkähler manifold.

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arXiv2014

N=2 supersymmetric gauge theories and quantum integrable systems

We study N=2 supersymmetric gauge theories on the product of a two-sphere and a cylinder. We show that the low-energy dynamics of a BPS sector of such a theory is described by a quantum integrable system, with the Planck constant set by the inverse of the radius of the sphere. If the sphere is replaced with a hemisphere, then our system reduces to an integrable system of the type studied by Nekrasov and Shatashvili. In this case we establish a correspondence between the effective prepotential of the gauge theory and the Yang-Yang function of the integrable system.

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arXiv2013

3d TQFT from 6d SCFT

We study the six-dimensional (2,0) superconformal field theory on S^1 x S^2 x M via compactification to five dimensions, where M is a three-manifold. Twisted along M, the five-dimensional theory has a half of N = (2,2) supersymmetry on S^2, the other half being broken by a superpotential. We show that in the limit where M is infinitely large, the twisted theory reduces to a three-dimensional topological quantum field theory which is closely related to Chern-Simons theory for the complexified gauge group.

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arXiv2013

Compactification on the Ω-background and the AGT correspondence

The six-dimensional (2,0) theory formulated in the Ω-background gives rise to two-dimensional effective degrees of freedom. By compactifying the theory on the circle fibers of two cigar-like manifolds, we find that a natural candidate for the effective theory is a chiral gauged WZW model. The symmetry algebra of the model contains the W-algebra that appears on the two-dimensional side of the AGT correspondence. We show that the expectation values of its currents determine the Seiberg-Witten curve of the four-dimensional side.

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arXiv2012

Chiral Algebras of (0,2) Models

We explore two-dimensional sigma models with (0,2) supersymmetry through their chiral algebras. Perturbatively, the chiral algebras of (0,2) models have a rich infinite-dimensional structure described by the cohomology of a sheaf of chiral differential operators. Nonperturbatively, instantons can deform this structure drastically. We show that under some conditions they even annihilate the whole algebra, thereby triggering the spontaneous breaking of supersymmetry. For a certain class of Kähler manifolds, this suggests that there are no harmonic spinors on their loop spaces and gives a physical proof of the Höhn-Stolz conjecture.

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arXiv2012

Vanishing Chiral Algebras and Höhn-Stolz Conjecture

Given a two-dimensional quantum field theory with (0,2) supersymmetry, one can construct a chiral (or vertex) algebra. The chiral algebra of a (0,2) supersymmetric sigma model is, perturbatively, the cohomology of a sheaf of chiral differential operators on a string Kähler manifold. However, it vanishes in some cases when instantons are taken into account. I will discuss the implication of this phenomenon for the Höhn-Stolz conjecture on the Witten genus.

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arXiv2012

On the six-dimensional origin of the AGT correspondence

We argue that the six-dimensional (2,0) superconformal theory defined on M \times C, with M being a four-manifold and C a Riemann surface, can be twisted in a way that makes it topological on M and holomorphic on C. Assuming the existence of such a twisted theory, we show that its chiral algebra contains a W-algebra when M = R^4, possibly in the presence of a codimension-two defect operator supported on R^2 \times C \subset M \times C. We expect this structure to survive the Ω-deformation.

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arXiv2008

Chiral Algebras of (0,2) Sigma Models: Beyond Perturbation Theory

We explore the nonperturbative aspects of the chiral algebras of N = (0,2) sigma models, which perturbatively are intimately related to the theory of chiral differential operators (CDOs). The grading by charge and scaling dimension is anomalous if the first Chern class of the target space is nonzero. This has some nontrivial consequences for the chiral algebra. As an example, we study the case where the target space is CP^1, and show that worldsheet instantons trivialize the chiral algebra entirely. Consequently, supersymmetry is spontaneously broken in this model. We then turn to a closer look at the supersymmetry breaking from the viewpoint of Morse theory on loop space. We find that instantons interpolate between pairs of perturbative supersymmetric states with different fermionic numbers, hence lifting them out of the supersymmetric spectrum. Our results reveal that a "quantum" deformation of the geometry of the target space leads to a trivialization of the kernels of certain twisted Dirac operators on CP^1.

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