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Liouville Correlation Functions from Four-Dimensional Gauge Theories

We conjecture an expression for the Liouville theory conformal blocks and correlation functions on a Riemann surface of genus g and n punctures as the Nekrasov partition function of a certain class…
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Reading between the lines of four-dimensional gauge theories

A bstractStarting with a choice of a gauge group in four dimensions, there is often freedom in the choice of magnetic and dyonic line operators. Different consistent choices of these operators…
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Comments on string theory backgrounds with non-relativistic conformal symmetry

We consider non-relativistic conformal quantum mechanical theories that arise by doing discrete light cone quantization of field theories. If the field theory has a gravity dual, then the conformal…
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Notes on the K3 Surface and the Mathieu Group M 24

We point out that the elliptic genus of the K3 surface has a natural decomposition in terms of dimensions of irreducible representations of the largest Mathieu group M 24. The reason remains a…
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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…
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Elliptic Genera of Two-Dimensional $${\mathcal{N} = 2}$$N=2 Gauge Theories with Rank-One Gauge Groups

We compute the elliptic genera of two-dimensional $${\mathcal{N} = (2, 2)}$$N=(2,2) and $${\mathcal{N} = (0, 2)}$$N=(0,2) -gauged linear sigma models via supersymmetric localization, for rank-one…
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Anomaly polynomial of general 6D SCFTs

We describe a method to determine the anomaly polynomials of general 6d N=(2,0) and N=(1,0) SCFTs, in terms of the anomaly matching on their tensor branches. This method is almost purely field…
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Central charges of 𝒩 = 2 superconformal field theories in four dimensions

We present a general method for computing the central charges a and c of N=2 superconformal field theories corresponding to singular points in the moduli space of N=2 gauge theories. Our method…
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Exactly marginal deformations and global symmetries

We study the problem of finding exactly marginal deformations of $ \mathcal{N} = 1 $ superconformal field theories in four dimensions. We find that the only way a marginal chiral operator can become…
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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…
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