arXiv subjects

Susanne Reffert

Publications and source records attributed to Susanne Reffert.

At least 55 records · Page 3Linked to original sources

arXiv2017

Monopole Quivers and new 3D N=2 dualities

We present a new family of dualities for three-dimensional gauge theories, motivated by the brane realization of the reduction of four-dimensional dualities on a circle. This family can be understood as a generalization of Aharony duality to quiver gauge theories whose nodes interact via monopole terms in the superpotential. We refer to this family of theories as monopole quivers. We corroborate the new dualities by checking the equivalence of the three-sphere partition functions, obtained from the standard circle reduction of the four-dimensional superconformal index. As a special case, we recover some dualities recently discussed in the literature.}

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arXiv2017

Compensating strong coupling with large charge

We study some (conformal) field theories with global symmetries in the sector where the value of the global charge $Q$ is large. We find (as expected) that the low energy excitations of this sector are described by the general form of Goldstone's theorem in the non-relativistic regime. We also derive the unexpected result, first presented in [Hellerman et al. 2015], that the effective field theory describing such sector of fixed $Q$ contains effective couplings $λ_{\text{eff}}\sim λ^b /Q^{a}$, where $λ$ is the original coupling. Hence, large charge leads to weak coupling. In the last section of the paper we present an outline of how to compute anomalous dimensions of the $O(n)$ model in this limit.

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arXiv2016

Generalized type IIB supergravity equations and non-Abelian classical r-matrices

We study Yang-Baxter deformations of the $AdS_5 \times S^5$ superstring with non-Abelian classical $r$-matrices which satisfy the homogeneous classical Yang-Baxter equation (CYBE). By performing a supercoset construction, we can get deformed $AdS_5 \times S^5$ backgrounds. While this is a new area of research, the current understanding is that Abelian classical $r$-matrices give rise to solutions of type IIB supergravity, while non-Abelian classical $r$-matrices lead to solutions of the generalized supergravity equations. We examine here some examples of non-Abelian classical r-matrices and derive the associated backgrounds explicitly. All of the resulting backgrounds satisfy the generalized equations. For some of them, we derive "T-dualized" backgrounds by adding a linear coordinate dependence to the dilaton and show that these satisfy the usual type IIB supergravity equations. Remarkably, some of the "T-dualized" backgrounds are locally identical to undeformed $AdS_5 \times S^5$ after an appropriate coordinate transformation, but this seems not to be generally the case.

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arXiv2016

Phases of N=2 Necklace Quivers

We classify the phases of N=2 elliptic models in terms of their global properties i.e. the spectrum of line operators. We show the agreement between the field theory and the M-theory analysis and how the phases form orbits under the action of the S-duality group which corresponds to the mapping class group of the Riemann surface in M-theory.

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arXiv2016

Line operators from M-branes on compact Riemann surfaces

In this paper, we determine the charge lattice of mutually local Wilson and 't Hooft line operators for class S theories living on M5-branes wrapped on compact Riemann surfaces. The main ingredients of our analysis are the fundamental group of the N-cover of the Riemann surface, and a quantum constraint on the six-dimensional theory. This latter plays a central role in excluding some of the possible lattices and imposing consistency conditions on the charges. This construction gives a geometric explanation for the mutual locality among the lines, fixing their charge lattice and the structure of the four-dimensional gauge group.

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arXiv2015

The braneology of 3D dualities

In this paper we study the reduction of four-dimensional Seiberg duality to three dimensions from a brane perspective. We reproduce the non-perturbative dynamics of the three-dimensional field theory via a T-duality at finite radius and the action of Euclidean D-strings. In this way we also overcome certain issues regarding the brane description of Aharony duality. Moreover we apply our strategy to more general dualities, such as toric duality for M2-branes and dualities with adjoint matter fields.

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arXiv2015

4D/3D reduction of dualities: mirrors on the circle

We engineer a brane picture for the reduction of Seiberg dualities from 4D to 3D, valid also in the presence of orientifold planes. We obtain effective 3D dualities on the circle by T-duality, geometrizing the non-perturbative superpotential which is an affine Toda potential. When reducing to pure 3D, we define a double-scaling limit which creates a confining sector, giving a unified mechanism for the brane reduction of dualities.

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arXiv2015

The M-theory origin of global properties of gauge theories

We show that global properties of gauge groups can be understood as geometric properties in M-theory. Different wrappings of a system of N M5-branes on a torus reduce to four-dimensional theories with $A_{N-1}$ gauge algebra and different unitary groups. The classical properties of the wrappings determine the global properties of the gauge theories without the need to impose any quantum conditions. We count the inequivalent wrappings as they fall into orbits of the modular group of the torus, which correspond to the S-duality orbits of the gauge theories.

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arXiv2015

Yang-Baxter deformations of Minkowski spacetime

We study Yang-Baxter deformations of 4D Minkowski spacetime. The Yang-Baxter sigma model description was originally developed for principal chiral models based on a modified classical Yang-Baxter equation. It has been extended to coset curved spaces and models based on the usual classical Yang-Baxter equation. On the other hand, for flat space, there is the obvious problem that the standard bilinear form degenerates if we employ the familiar coset Poincaré group/Lorentz group. Instead we consider a slice of AdS$_5$ by embedding the 4D Poincaré group into the 4D conformal group $SO(2,4)$. With this procedure we obtain metrics and $B$-fields as Yang-Baxter deformations which correspond to well-known configurations such as T-duals of Melvin backgrounds, Hashimoto-Sethi and Spradlin-Takayanagi-Volovich backgrounds, the T-dual of Grant space, pp-waves, and T-duals of dS$_4$ and AdS$_4$. Finally we consider a deformation with a classical $r$-matrix of Drinfeld-Jimbo type and explicitly derive the associated metric and $B$-field which we conjecture to correspond to a new integrable system.

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arXiv2014

Alpha- and Omega-Deformations from fluxes in M-Theory

We discuss an SL(2,R) family of deformed N=2 four-dimensional gauge theories which we derive from a flux background in M-theory. In addition to the Omega-deformation this family includes a new deformation, which we call the Alpha-deformation, which can be viewed as an S-dual to the Omega-deformation. We study these gauge theories in two ways: by constructing a non-Abelian (but UV-complete) Lagrangian, and by their strong coupling lift to M-theory where their low-energy dynamics can be determined by examining the equation of motion of a single M5-brane wrapped on a Riemann surface.

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arXiv2013

Deformed supersymmetric gauge theories from the fluxtrap background

The fluxtrap background of string theory provides a transparent and algorithmic way of constructing supersymmetric gauge theories with both mass and Omega-type deformations in various dimensions. In this article, we review a number of deformed supersymmetric gauge theories in two and four dimensions which can be obtained via the fluxtrap background from string or M-theory. Such theories, the most well-known being Omega-deformed super Yang-Mills theory in four dimensions, have met with a lot of interest in the recent literature. The string theory treatment offers many new avenues of analysis and applications, such as for example the study of the gravity duals for deformed N=4 gauge theories.

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arXiv2013

BPS States in the Duality Web of the Omega deformation

In this note, we study different limits of an Omega-deformed (2,0) six-dimensional gauge theory realized in a M-theory fluxtrap background. Via a chain of dualities, we connect the Omega-deformed SYM to a new four-dimensional gauge theory which we refer to as the reciprocal gauge theory. This theory has several properties in common with Liouville field theory, such as its gauge coupling b^2 =ε_2 / ε_1, and its behavior under S-duality. Finally, we realize the BPS states on the SYM side of the AGT correspondence and follow them along the chain of dualities. In the fluxtrap frame, we are dealing with two distinct types of states localized in different radial positions, while in the reciprocal frame, we find single states carrying both charges localized in one place which appear to be perturbatively stable. Our microscopic picture of the small-b limit exhibits semiclassically BPS bound states, which are not visible at the level of the partition function.

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arXiv2013

Omega-Deformed Seiberg-Witten Effective Action from the M5-brane

We obtain the leading order corrections to the effective action of an M5-brane wrapping a Riemann surface in the eleven-dimensional supergravity Omega-background. The result can be identified with the first order epsilon-deformation of the Seiberg-Witten effective action of pure SU(2) gauge theory. We also comment on the second order corrections and the generalization to arbitrary gauge group and matter content.

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arXiv2012

The Omega Deformation From String and M-Theory

We present a string theory construction of Omega-deformed four-dimensional gauge theories with generic values of ε_1 and ε_2. Our solution gives an explicit description of the geometry in the core of Nekrasov and Witten's realization of the instanton partition function, far from the asymptotic region of their background. This construction lifts naturally to M-theory and corresponds to an M5-brane wrapped on a Riemann surface with a selfdual flux. Via a 9-11 flip, we finally reinterpret the Omega deformation in terms of non-commutative geometry. Our solution generates all modified couplings of the Ω-deformed gauge theory, and also yields a geometric origin for the quantum spectral curve of the associated quantum integrable system.

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arXiv2012

General Omega Deformations from Closed String Backgrounds

In this note, an important extension to the recent construction of the fluxtrap background is presented. The fluxtrap is a closed string background based on the Melvin solution corresponding to the Omega deformation of flat space. In this note, we introduce the mechanisms to extend it from epsilon_1=-epsilon_2 in R to more general values of epsilon_1 and epsilon_2 in C.

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arXiv2012

String theory of the Omega deformation

In this article, we construct a supersymmetric real mass deformation for the adjoint chiral multiplets in the gauge theory describing the dynamics of a stack of D2-branes in type II string theory. We do so by placing the D2-branes into the T-dual of a supersymmetric NS fluxbrane background. We furthermore note that this background is the string theoretic realization of an Omega-deformation of flat space in the directions transverse to the branes where the deformation parameters satisfy ε_1 = - ε_2. This Ω-deformation therefore serves to give supersymmetric real masses to the chiral multiplets of the 3D gauge theory. To illustrate the physical effect of the real mass term, we derive BPS-saturated classical solutions for the branes rotating in this background. Finally, we reproduce all the same structure in the presence of NS fivebranes and comment on the relationship to the gauge theory/spin-chain correspondence of Nekrasov and Shatashvili.

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arXiv2011

Twisted Masses and Enhanced Symmetries: the A&D Series

We study new symmetries between A and D type quiver gauge theories with different numbers of colors. We realize these gauge theories with twisted masses via a brane construction that reproduces all the parameters of the Gauge/Bethe correspondence.

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arXiv2010

The Gauge-Bethe Correspondence and Geometric Representation Theory

The Gauge/Bethe correspondence of Nekrasov and Shatashvili relates the spectrum of integrable spin chains to the ground states of supersymmetric gauge theories. Up to now, this correspondence has been an observation; the underlying reason for its existence remaining elusive. We argue here that geometrical representation theory is the mathematical foundation of the Gauge/Bethe correspondence, and it provides a framework to study families of gauge theories in a unified way.

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