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On Three Dimensional Quiver Gauge Theories and Integrability
"... In this work we compare different descriptions of the space of vacua of certain three dimensional N = 4 superconformal field theories, compactified on a circle and massdeformed to N = 2 in a canonical way. The original N = 4 theories are known to admit two distinct mirror descriptions as linear q ..."
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In this work we compare different descriptions of the space of vacua of certain three dimensional N = 4 superconformal field theories, compactified on a circle and massdeformed to N = 2 in a canonical way. The original N = 4 theories are known to admit two distinct mirror descriptions as linear quiver gauge theories, and many more descriptions which involve the compactification on a segment of fourdimensional N = 4 super YangMills theory. Each description gives a distinct presentation of the moduli space of vacua. Our main result is to establish the precise dictionary between these presentations. We also study the relationship between this gauge theory problem and integrable systems. The space of vacua in the linear quiver gauge theory description is related by NekrasovShatashvili duality to the eigenvalues of quantum integrable spin chain Hamiltonians. The space of vacua in the fourdimensional gauge theory description is related to the solution of certain integrable classical manybody problems. Thus we obtain numerous dualities between these integrable models. ar X iv
Anomalous dimensions of monopole operators in threedimensional quantum electrodynamics
"... The space of local operators in threedimensional quantum electrodynamics contains monopole operators that create n units of gauge flux emanating from the insertion point. This paper uses the stateoperator correspondence to calculate the anomalous dimensions of these monopole operators perturbative ..."
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The space of local operators in threedimensional quantum electrodynamics contains monopole operators that create n units of gauge flux emanating from the insertion point. This paper uses the stateoperator correspondence to calculate the anomalous dimensions of these monopole operators perturbatively to nexttoleading order in the 1/Nf expansion, thus improving on the existing leading order results in the literature. Here, Nf is the number of twocomponent complex fermion flavors. The scaling dimension of the n = 1 monopole operator is 0.265Nf − 0.0383 +O(1/Nf) at the infrared conformal fixed point.
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"... A relevant perturbation of the entanglement entropy of a sphere is examined holographically near the UV fixed point. Varying the conformal dimension of the relevant operator, we obtain three different sectors: 1) the entanglement entropy is stationary and the perturbative expansion is welldefined ..."
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A relevant perturbation of the entanglement entropy of a sphere is examined holographically near the UV fixed point. Varying the conformal dimension of the relevant operator, we obtain three different sectors: 1) the entanglement entropy is stationary and the perturbative expansion is welldefined with respect to the relevant coupling, 2) the entropy is stationary, but the perturbation fails, 3) the entropy is neither stationary nor perturbative. We compare our holographic results with the numerical calculation for a free massive scalar field in threedimensions, and find a qualitative agreement between them. We speculate that these statements hold for any relevant perturbation in any quantum field theory invariant under the Poincare ́ symmetry.