arXiv subjects

Yuji Tachikawa

Publications and source records attributed to Yuji Tachikawa.

At least 109 records · Page 6Linked to original sources

arXiv2013

2d SCFTs from M2-branes

We consider the low-energy limit of the two-dimensional theory on k M2-branes suspended between a straight M5-brane and a curved M5-brane. We argue that it is described by an N=(2,2) supersymmetric gauge theory with no matter fields but with a non-trivial twisted superpotential, and also by an N=(2,2) supersymmetric Landau-Ginzburg model, such that the (twisted) superpotentials are determined by the shape of the M5-branes. We find particular cases realize Kazama-Suzuki models. Evidence is provided by the study of ground states, chiral rings, BPS spectra and S^2 partition functions of the systems.

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arXiv2013

N=1 dynamics with T_N theory

We study the dynamics of N=1 supersymmetric systems consisting of the strongly-coupled superconformal theory T_N, SU(N) gauge groups, and fundamental chiral multiplets. We demonstrate that such systems exhibit familiar phenomena such as deformation of the vacuum moduli space, appearance of the dynamical superpotential, and Coulomb branches with N=1 Seiberg-Witten curves. The analysis requires a rather detailed knowledge of the chiral ring of the T_N theory, which will also be discussed at length.

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arXiv2013

Elliptic genera of 2d N=2 gauge theories

We compute the elliptic genera of general two-dimensional N=(2,2) and N=(0,2) gauge theories. We find that the elliptic genus is given by the sum of Jeffrey-Kirwan residues of a meromorphic form, representing the one-loop determinant of fields, on the moduli space of flat connections on T^2. We give several examples illustrating our formula, with both Abelian and non-Abelian gauge groups, and discuss some dualities for U(k) and SU(k) theories. This paper is a sequel to the authors' previous paper arXiv:1305.0533.

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arXiv2013

Elliptic genera of two-dimensional N=2 gauge theories with rank-one gauge groups

We compute the elliptic genera of two-dimensional N=(2,2) and N=(0,2) gauged linear sigma models via supersymmetric localization, for rank-one gauge groups. The elliptic genus is expressed as a sum over residues of a meromorphic function whose argument is the holonomy of the gauge field along both the spatial and the temporal directions of the torus. We illustrate our formulas by a few examples including the quintic Calabi-Yau, N=(2,2) SU(2) and O(2) gauge theories coupled to N fundamental chiral multiplets, and a geometric N=(0,2) model.

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arXiv2013

Dynamical Supersymmetry Breaking with T_N Theory

We demonstrate that the supersymmetry is dynamically broken in the four-dimensional SU(N) gauge theory coupled to a strongly-coupled superconformal theory T_N. This is a direct generalization of the model of supersymmetry breaking on deformed moduli space in supersymmetric QCD with an SU(2) gauge group.

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arXiv2013

Notes on reductions of superstring theory to bosonic string theory

It is in general very subtle to integrate over the odd moduli of super Riemann surfaces in perturbative superstring computations. We study how these subtleties go away in favorable cases, including the embedding of N=0 string to N=1 string by Berkovits and Vafa, and the relation of the graviphoton amplitude and the topological string amplitude by Antoniadis, Gava, Narain and Taylor and Bershadsky, Cecotti, Ooguri and Vafa. The Poincaré dual of the moduli space of Riemann surfaces in the moduli space of super Riemann surfaces plays an important role.

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arXiv2013

Superconformal Indices, Sasaki-Einstein Manifolds, and Cyclic Homologies

The superconformal index of the quiver gauge theory dual to type IIB string theory on the product of an arbitrary smooth Sasaki-Einstein manifold with five-dimensional AdS space is calculated both from the gauge theory and gravity viewpoints. We find complete agreement. Along the way, we find that the index on the gravity side can be expressed in terms of the Kohn-Rossi cohomology of the Sasaki-Einstein manifold and that the index of a quiver gauge theory equals the Euler characteristic of the cyclic homology of the Ginzburg dg algebra associated to the quiver.

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arXiv2013

New N=1 Dualities

We show that the N=1 supersymmetric SU(N) gauge theory with 2N flavors without superpotential has not only the standard Seiberg dual description but also another dual description involving two copies of the so-called T_N theory. This is a natural generalization to N>2 of a dual description of SU(2) gauge theory with 4 flavors found by Csaki, Schmaltz, Skiba and Terning. We also study dualities of other N=1 SCFTs involving copies of T_N theories. Our duality is the basic operation from which a recently-found web of N=1 dualities obtained by compactifying M5-branes on Riemann surfaces can be derived field-theoretically.

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arXiv2012

Gaiotto Duality for the Twisted A_{2N-1} Series

We study 4D N=2 superconformal theories that arise from the compactification of 6D N=(2,0) theories of type A_{2N-1} on a Riemann surface C, in the presence of punctures twisted by a Z_2 outer automorphism. We describe how to do a complete classification of these SCFTs in terms of three-punctured spheres and cylinders, which we do explicitly for A_3, and provide tables of properties of twisted defects up through A_9. We find atypical degenerations of Riemann surfaces that do not lead to weakly-coupled gauge groups, but to a gauge coupling pinned at a point in the interior of moduli space. As applications, we study: i) 6D representations of 4D superconformal quivers in the shape of an affine/non-affine D_n Dynkin diagram, ii) S-duality of SU(4) and Sp(2) gauge theories with various combinations of fundamental and antisymmetric matter, and iii) realizations of all rank-one SCFTs predicted by Argyres and Wittig.

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arXiv2012

2d TQFT structure of the superconformal indices with outer-automorphism twists

We study the superconformal indices of 4d theories coming from 6d N=(2,0) theory of type Γon a Riemann surface, with the action of the outer-automorphism σin the trace. We find that the indices are given by the partition function of a deformed 2d Yang-Mills on the Riemann surface with gauge group G which is S-dual to the subgroup of Γfixed by σ. In the 2-parameter deformed version, we find that it is governed not by Macdonald polynomials of type G, but by Macdonald polynomials associated to twisted affine root systems.

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arXiv2012

4d partition function on S^1 x S^3 and 2d Yang-Mills with nonzero area

We argue that 6d N=(2,0) theory on S^1 x S^3 x C_2 reduces to the 2d q-deformed Yang-Mills on C_2 at finite area, as a small extension to the result of Gadde, Rastelli, Razamat and Yan. This is done by computing the partition function on S^1 x S^3 of 4d N=2 supersymmetric non-linear sigma model on T^*G_C, which gives the propagator of the 2d Yang-Mills.

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arXiv2012

Quantum Higgs branches of isolated N=2 superconformal field theories

We study the Higgs branches of the superconformal points of four-dimensional N=2 super Yang-Mills (SYM) which appear due to the occurrence of mutually local monopoles having appropriate charges. We show, for example, that the maximal superconformal point of SU(2n) SYM has a Higgs branch of the form C^2/Z_n. These Higgs branches are intrinsic to the superconformal field theory (SCFT) at the superconformal point, but do not appear in the SYM theory in which it is embedded. This is because the embedding is a UV extension of the SCFT in which some global symmetry acting on the Higgs branch is gauged irrelevantly. Higgs branches deduced from earlier direct studies of these isolated SCFTs using BPS wall-crossing or 3-d mirror symmetry agree with the ones we find here using just the Seiberg-Witten data for the SYM theories.

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arXiv2012

Nilpotent orbits and codimension-two defects of 6d N=(2,0) theories

We study the local properties of a class of codimension-2 defects of the 6d N=(2,0) theories of type J=A,D,E labeled by nilpotent orbits of a Lie algebra \mathfrak{g}, where \mathfrak{g} is determined by J and the outer-automorphism twist around the defect. This class is a natural generalisation of the defects of the 6d theory of type SU(N) labeled by a Young diagram with N boxes. For any of these defects, we determine its contribution to the dimension of the Higgs branch, to the Coulomb branch operators and their scaling dimensions, to the 4d central charges a and c, and to the flavour central charge k.

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arXiv2011

On S-duality of 5d super Yang-Mills on S^1

We study a duality of 5d maximally supersymmetric Yang-Mills on S^1, which exchanges the tower of Kaluza-Klein W-bosons and the tower of instantonic monopoles. This duality maps a non-simply-laced gauge theory to a simply-laced gauge theory twisted by an outer automorphism around S^1, and is closely related to the Langlands dual of affine Lie algebras. We also discuss how this S-duality is implemented in terms of 6d N=(2,0) theory. This is straightforward except for the 6d theory of type SU(2n+1) with Z_2 outer-automorphism twist, for which a few new properties are deduced. For example, this 6d theory, when reduced on an S^1 with Z_2 twist, gives 5d USp(2n) theory with nontrivial discrete 5d theta angle.

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arXiv2011

On 6d N=(2,0) theory compactified on a Riemann surface with finite area

We study 6d N=(2,0) theory of type SU(N) compactified on Riemann surfaces with finite area, including spheres with fewer than three punctures. The Higgs branch, whose metric is inversely proportional to the total area of the Riemann surface, is discussed in detail. We show that the zero-area limit, which gives us a genuine 4d theory, can involve a Wigner-Inonu contraction of global symmetries of the six-dimensional theory. We show how this explains why subgroups of SU(N) can appear as the gauge group in the 4d limit. As a by-product we suggest that half-BPS codimension-two defects in the six-dimensional (2,0) theory have an operator product expansion whose operator product coefficients are four-dimensional field theories.

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arXiv2011

A strange relationship between 2d CFT and 4d gauge theory

A relationship between 4d gauge theory and 2d CFT will be reviewed from the very basics. We will first cover the introductory material on the 2d CFT and on the instantons of 4d gauge theory. Next we will explicitly calculate and check the agreement of the norm of a coherent state on the 2d side and the instanton partition function on the 4d side. We will then see how this agreement can be understood from the perspective of string and M theory.

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arXiv2011

Seiberg-Witten Geometries Revisited

We provide a uniform solution to 4d N=2 gauge theory with a single gauge group G=A,D,E when the one-loop contribution to the beta function from any irreducible component R of the hypermultiplets is less than or equal to half of that of the adjoint representation. The solution is given by a non-compact Calabi-Yau geometry, whose defining equation is built from explicitly known polynomials W_G and X_R, associated respectively to the gauge group G and each irreducible component R. We provide many pieces of supporting evidence, for example by analyzing the system from the point of view of the 6d N=(2,0) theory compactified on a sphere.

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arXiv2011

On 2d TQFTs whose values are holomorphic symplectic varieties

For simple and simply-connected complex algebraic group G, we conjecture the existence of a functor eta_G from the category of 2-bordisms to the category of holomorphic symplectic varieties with Hamiltonian action, such that gluing of boundaries corresponds to the holomorphic symplectic quotient with respect to the diagonal action of G. We describe various properties of eta_G obtained via string-theoretic analysis. Mathematicians are urged to construct eta_G rigorously.

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