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13 papers found.
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Mirror symmetry and loop operators

Wilson loops in gauge theories pose a fundamental challenge for dualities. Wilson loops are labeled by a representation of the gauge group and should map under duality to loop operators labeled by the same data, yet generically, dual theories have completely different gauge groups. In this paper we resolve this conundrum for three dimensional mirror symmetry. We show that Wilson...

M2-brane surface operators and gauge theory dualities in Toda

We give a microscopic two dimensional \( \mathcal{N} \) = (2, 2) gauge theory description of arbitrary M2-branes ending on N f M5-branes wrapping a punctured Riemann surface. These realize surface operators in four dimensional \( \mathcal{N} \) = 2 field theories. We show that the expectation value of these surface operators on the sphere is captured by a Toda CFT correlation...

Shortening anomalies in supersymmetric theories

We present new anomalies in two-dimensional \( \mathcal{N}=\left(2,2\right) \) superconformal theories. They obstruct the shortening conditions of chiral and twisted chiral multiplets at coincident points. This implies that marginal couplings cannot be promoted to background superfields in short representations. Therefore, standard results that follow from \( \mathcal{N}=\left(2...

Kähler potential and ambiguities in 4d \( \mathcal{N} \) = 2 SCFTs

The partition function of four-dimensional \( \mathcal{N} \) = 2 superconformal field theories on S 4 computes the exact Kähler potential on the space of exactly marginal couplings [1]. We present a new elementary proof of this result using supersymmetry Ward identities. The partition function is a section rather than a function, and is subject to ambiguities coming from Kähler...

Correlation functions of Coulomb branch operators

We consider the correlation functions of Coulomb branch operators in four-dimensional \( \mathcal{N} \) = 2 Superconformal Field Theories (SCFTs) involving exactly one antichiral operator. These extremal correlators are the “minimal” non-holomorphic local observables in the theory. We show that they can be expressed in terms of certain determinants of derivatives of the four...

Sphere partition functions and the Zamolodchikov metric

We study the finite part of the sphere partition function of d-dimensional Conformal Field Theories (CFTs) as a function of exactly marginal couplings. In odd dimensions, this quantity is physical and independent of the exactly marginal couplings. In even dimensions, this object is generally regularization scheme dependent and thus unphysical. However, in the presence of...

Anomalies, conformal manifolds, and spheres

The two-point function of exactly marginal operators leads to a universal contribution to the trace anomaly in even dimensions. We study aspects of this trace anomaly, emphasizing its interpretation as a sigma model, whose target space \( \mathrm{\mathcal{M}} \) is the space of conformal field theories (a.k.a. the conformal manifold). When the underlying quantum field theory is...

’t Hooft operators in gauge theory from Toda CFT

We construct loop operators in two dimensional Toda CFT and calculate with them the exact expectation value of certain supersymmetric ’t Hooft and dyonic loop operators in four dimensional \( \mathcal{N} = 2 \) gauge theories with SU(N) gauge group. Explicit formulae for ’t Hooft and dyonic operators in \( \mathcal{N} = 2 * \) and \( \mathcal{N} = 2 \) conformal SQCD with SU(N...

Exact results for ’t Hooft loops in Gauge theories on S 4

The path integral of a general \(\mathcal{N} = 2\) supersymmetric gauge theory on S 4 is exactly evaluated in the presence of a supersymmetric ’t Hooft loop operator. The result we find — obtained using localization techniques — captures all perturbative quantum corrections as well as non-perturbative effects due to instantons and monopoles, which are supported at the north pole...

Exact results in D = 2 supersymmetric gauge theories

We compute exactly the partition function of two dimensional \( \mathcal{N} \) = (2, 2) gauge theories on S 2 and show that it admits two dual descriptions: either as an integral over the Coulomb branch or as a sum over vortex and anti-vortex excitations on the Higgs branches of the theory. We further demonstrate that correlation functions in two dimensional Liouville/Toda CFT...

IIB duals of D = 3 \( \mathcal{N} = 4 \) circular quivers

We construct the type-IIB AdS4 ⋉ K supergravity solutions which are dual to the three-dimensional \( \mathcal{N} = 4 \) superconformal field theories that arise as infrared fixed points of circular-quiver gauge theories. These superconformal field theories are labeled by a triple \( \left( {\rho, \hat{\rho},L} \right) \) subject to constraints, where ρ and \( \hat{\rho} \) are...

Holographic duals of D = 3 \( \mathcal{N} = 4 \) superconformal field theories

We find the warped AdS 4 ⋉ K type-IIB supergravity solutions holographically dual to a large family of three dimensional \( \mathcal{N} = 4 \) superconformal field theories labeled by a pair \( \left( {\rho, \hat{\rho }} \right) \) of partitions of N. These superconformal theories arise as renormalization group fixed points of three dimensional mirror symmetric quiver gauge...

Gauge theory loop operators and Liouville theory

We propose a correspondence between loop operators in a family of four dimensional \( \mathcal{N} \) = 2 gauge theories on S 4 — including Wilson, ‘t Hooft and dyonic operators — and Liouville theory loop operators on a Riemann surface. This extends the beautiful relation between the partition function of these \( \mathcal{N} \) = 2 gauge theories and Liouville correlators found...