Dual Gauge Group Research Articles

On the dynamical origin of the η′ potential and the axion mass

We investigate the dynamics responsible for generating the potential of the η′, the (would-be) Goldstone boson associated with the anomalous axial U(1) symmetry of QCD. The standard lore posits that pure QCD dynamics generates a confining potential with a branched structure as a function of the θ angle, and that this same potential largely determines the properties of the η′ once fermions are included. Here we test this picture by examining a supersymmetric extension of QCD with a small amount of supersymmetry breaking generated via anomaly mediation. For pure SU(N) QCD without flavors, we verify that there are N branches generated by gaugino condensation. Once quarks are introduced, the flavor effects qualitatively change the strong dynamics of the pure theory. For F flavors we find |N − F| branches, whose dynamical origin is gaugino condensation in the unbroken subgroup for F < N – 1, and in the dual gauge group for F > N + 1. For the special cases of F = N – 1, N, N + 1 we find no branches and the entire potential is consistent with being a one-instanton effect. The number of branches is a simple consequence of the selection rules of an anomalous U(1)R symmetry. We find that the η′ mass does not vanish in the large N limit for fixed F/N, since the anomaly is non-vanishing. The same dynamics that is responsible for the η′ potential is also responsible for the axion potential. We present a simple derivation of the axion mass formula for an arbitrary number of flavors.

Abelian Duality for Generalized Maxwell Theories

We describe a construction of generalized Maxwell theories -- higher analogues of abelian gauge theories -- in the factorization algebra formalism of Costello and Gwilliam, allowing for analysis of the structure of local observables. We describe the phenomenon of abelian duality for local observables in these theories as a form of Fourier duality, relating observables in theories with dual abelian gauge groups and inverted coupling constants in a way compatible with the local structure. We give a description of expectation values in this theory and prove that duality preserves expectation values. Duality is shown to, for instance, interchange higher analogues of Wilson and 't Hooft operators.

On the connection between hydrodynamics and quantum chaos in holographic theories with stringy corrections

Pole-skipping is a recently discovered signature of many-body quantum chaos in collective energy dynamics. It establishes a precise connection between resummed, all-order hydrodynamics and the underlying microscopic chaos. In this paper, we demonstrate the existence of pole-skipping in holographic conformal field theories with higher-derivative gravity duals. In particular, we first consider Einstein-Hilbert gravity deformed by curvature-squared (R2) corrections and then type IIB supergravity theory with the α′ 3R4 term, where α′ is set by the length of the fundamental string. The former case allows us to discuss the effects of leading-order 1/Nc corrections (with Nc being the number of colours of the dual gauge group) and phenomenological coupling constant dependence. In Einstein-Gauss-Bonnet theory, pole-skipping turns out to be valid non-perturbatively in the Gauss-Bonnet coupling. The α′ 3R4 deformation enables us to study perturbative inverse ’t Hooft coupling corrections (α′ 3 ∼ 1/λ3/2) in SU(Nc), mathcal{N}=4 supersymmetric Yang-Mills theory with infinite Nc. While the maximal Lyapunov exponent characterising quantum chaos remains uncorrected, the butterfly velocity is shown to depend both on Nc and the coupling. Several implications of the relation between hydrodynamics and chaos are discussed, including an intriguing similarity between the dependence of the butterfly velocity and the ratio of shear viscosity to entropy density on stringy corrections.

Anomaly constraints on deconfinement and chiral phase transition

We study constraints on thermal phase transitions of ${\rm SU}(N_c)$ gauge theories by using the 't Hooft anomaly involving the center symmetry and chiral symmetry. We consider two cases of massless fermions: (i) adjoint fermions, and (ii) $N_f$ flavors of fundamental fermions with a nontrivial greatest common divisor ${\rm gcd}(N_c,N_f) \neq 1$. For the first case (i), we show that the chiral symmetry restoration in terms of the standard Landau-Ginzburg effective action is impossible at a temperature lower than that of deconfinement. For the second case (ii), we introduce a modified version of the center symmetry which we call center-flavor symmetry, and draw similar conclusions under a certain definition of confinement. Moreover, at zero temperature, our results give a partial explanation of the appearance of dual magnetic gauge group in (supersymmetric) QCD when ${\rm gcd}(N_c,N_f) \neq 1$.

Darboux coordinates, Yang-Yang functional, and gauge theory

The moduli space of flat SL 2 connections on a punctured Riemann surface Σ with fixed conjugacy classes of the monodromies around the punctures is endowed with a system of holomorphic Darboux coordinates in which the generating function of the variety of SL 2 -opers is identified with the universal part of the effective twisted superpotential of the corresponding four-dimensional N=2 supersymmetric theory subject to the two-dimensional Ω-deformation. This allows defining the Yang-Yang functionals for the quantum Hitchin system in terms of the classical geometry of the moduli space of local systems for the dual gauge group and relating it to the instanton counting of the four-dimensional gauge theories in the rank-one case.

On O(N c) d = 3 $ \mathcal{N} = 2 $ supersymmetric QCD theories

We study three dimensional N=2 supersymmetric QCD theories with O(N_c) gauge groups and with N_f chiral multiplets in the vector representation. We argue that for N_f < N_c-2 there is a runaway potential on the moduli space and no vacuum. For N_f >= N_c-2 there is a moduli space also in the quantum theory, and for N_f >= N_c-1 there is a superconformal fixed point at the origin of this moduli space that has a dual description as the low-energy fixed point of an O(N_f-N_c+2) gauge theory. We test this duality in various ways; in some cases the duality for an O(2) gauge theory may be related to the known duality for U(1) gauge theories. We also discuss real mass deformations, which allow to connect theories with a different Chern-Simons level. This allows us to connect our duality with the known duality in O(N_c) theories with a Chern-Simons term of level k, where the dual gauge group is given by O(N_f+|k|-N_c+2).

A fat Higgs with a magnetic personality

We introduce a novel composite Higgs theory based on confining supersymmetric QCD. Supersymmetric duality plays a key role in this construction, with a "fat" Higgs boson emerging as a dual magnetic degree of freedom charged under the dual magnetic gauge group. Due to spontaneous color-flavor locking in the infrared, the electroweak gauge symmetry is aligned with the dual magnetic gauge group, allowing large Yukawa couplings between elementary matter fields and the composite Higgs. At the same time, this theory exhibits metastable supersymmetry breaking, leading to low-scale gauge mediation via composite messengers. The Higgs boson is heavier than in minimal supersymmetric theories, due to non-decoupling D-terms and a large F-term quartic coupling. This theory predicts quasi-stable TeV-scale pseudo-modulini, some of which are charged under standard model color, possibly giving rise to long-lived R-hadrons at the LHC.

Darboux coordinates, Yang-Yang functional, and gauge theory

The moduli space of SL(2) flat connections on a punctured Riemann surface with the fixed conjugacy classes of the monodromies around the punctures is endowed with a system of holomorphic Darboux coordinates, in which the generating function of the variety of SL(2)-opers is identified with the universal part of the effective twisted superpotential of the corresponding four dimensional N=2 supersymmetric theory subject to the two-dimensional Omega-deformation. This allows to give a definition of the Yang-Yang functionals for the quantum Hitchin system in terms of the classical geometry of the moduli space of local systems for the dual gauge group, and connect it to the instanton counting of the four dimensional gauge theories, in the rank one case.

Non-Abelian confinement inN=2supersymmetric QCD: Duality and kinks on confining strings

Recently we observed a crossover transition (in the Fayet-Iliopoulos parameter) from weak to strong coupling in N=2 supersymmetric QCD with the U(N) gauge group and N_f > N quark flavors. At strong coupling this theory can be described by a dual non-Abelian weakly coupled SQCD with the dual gauge group U(N_f-N) and N_f light dyon flavors. Both theories support non-Abelian strings. We continue the study of confinement dynamics in these theories, in particular, metamorphoses of excitation spectra, from a different side. A number of results obtained previously are explained, enhanced and supplemented by analyzing the world-sheet dynamics on the non-Abelian confining strings. The world-sheet theory is the two-dimensional N=(2,2) supersymmetric weighted CP(N_f-1) model. We explore the vacuum structure and kinks on the world sheet, corresponding to confined monopoles in the bulk theory. We show that (in the equal quark mass limit) these kinks fall into the fundamental representation of the unbroken global SU(N)\times SU(N_f-N)\timesU(1) group. This result confirms the presence of "extra" stringy meson states in the adjoint representation of the global group in the bulk theory. The non-Abelian bulk duality is in one-to-one correspondence with a duality taking place in the N=(2,2) supersymmetric weighted CP(N_f-1) model.

Higher representations duals

We uncover novel solutions of the 't Hooft anomaly matching conditions for scalarless gauge theories with matter transforming according to higher dimensional representations of the underlying gauge group. We argue that, if the duals exist, they are gauge theories with fermions transforming according to the defining representation of the dual gauge group. The resulting conformal windows match the one stemming from the all-orders beta function results when taking the anomalous dimension of the fermion mass to be unity which are also very close to the ones obtained using the Schwinger–Dyson approximation. We use the solutions to gain useful insight on the conformal window of the associated electric theory. A consistent picture emerges corroborating previous results obtained via different analytic methods and in agreement with first principle lattice explorations.

The phase structure of supersymmetric Sp(2Nc) gauge theories with an adjoint

We study the phase structure of = 1 supersymmetric Sp(2Nc) gauge theories with 2Nf fundamentals, an adjoint, and vanishing superpotential. Using a-maximization, we derive analytic expressions for the values of Nf below which the first several gauge-invariant operators in the chiral ring violate the unitarity bound and become free fields. In doing so we are able to explicitly check previous conjectures about the behavior of this theory made by Luty, Schmaltz, and Terning. We then compare this to an analysis of the first two 'deconfined' dual descriptions based on the gauge groups Sp(2Nf+2) × SO(2Nc+5) and Sp(2Nf+2) × SO(4Nf+4) × Sp(2Nc+2), finding precise agreement. In particular, we find no evidence for non-obvious accidental symmetries or the appearance of a mixed phase in which one of the dual gauge groups becomes free.

Non-Abelian duality and confinement inN=2supersymmetric QCD

In N=2 supersymmetric QCD with the U(N) gauge group and N_f>N we study the crossover transition from the weak coupling regime at large \xi to strong coupling at small \xi where \xi is the Fayet--Iliopoulos parameter. We find that at strong coupling a dual non-Abelian weakly coupled N=2 theory exists which describes low-energy physics at small \xi. The dual gauge group is U(N_f-N) and the dual theory has N_f flavors of light dyons, to be compared with N_f quarks in the original U(N) theory. Both, the original and dual theories are Higgsed and share the same global symmetry SU(N) x SU(N_f-N) x U(1), albeit the physical meaning of the SU(N) and SU(N_f-N) factors is different in the large- and small-\xi regimes. Both regimes support non-Abelian semilocal strings. In each of these two regimes particles that are in the adjoint representations with respect to one of the factor groups exist in two varieties: elementary fields and composite states bound by strings. These varieties interchange upon transition from one regime to the other. We conjecture that the composite stringy states can be related to Seiberg's M fields. The bulk duality that we observed translates into a two-dimensional duality on the world sheet of the non-Abelian strings. At large \xi the internal dynamics of the semilocal non-Abelian strings is described by the sigma model of N orientational and (N_f-N) size moduli, while at small \xi the roles of orientational and size moduli interchange. The BPS spectra of two dual sigma models (describing confined monopoles/dyons of the bulk theory) coincide. It would be interesting to trace parallels between the non-Abelian duality we found and string theory constructions.

NON-ABELIAN VORTEX AND CONFINEMENT

We discuss general properties and possible types of magnetic vortices in non-Abelian gauge theories (we consider here G = SU (N), SO (N), USp (2N)) in the Higgs phase. The sources of such vortices carry "fractional" quantum numbers such as Zn charge (for SU (N)), but also full non-Abelian charges of the dual gauge group. If such a model emerges as an effective dual magnetic theory of the fundamental (electric) theory, the non-Abelian vortices can provide for the mechanism of quark confinement in the latter.

Some simpler analogues of the dual standard model and their relation to Bais' generalisation of the Montonen–Olive conjecture

We show that the correspondence between SU(5) monopoles and the elementary particles, which underlies the construction of a dual standard model, has some simpler analogues associated with the strong, weak and hypercharge interactions. We then discuss how these analogues relate to Bais' generalization of the Montenon-Olive conjecture and find the representations of the monopoles under the dual gauge group; these representations agree with those of the elementary particles.

Duality between simple-group gauge theories and some applications

In this paper we investigate N=1 supersymmetric gauge theories with a product gauge group. By using smoothly confining dynamics, we can find new dualities which include higher-rank tensor fields, and in which the dual gauge group is simple, not a product. Some of them are dualities between chiral and non-chiral gauge theories. We also discuss some applications to dynamical supersymmetry breaking phenomena and new confining theories with a tree-level superpotential.

Duality, phases, spinors and monopoles in SO(N) and spin(N) gauge theories

Four-dimensional N=1 supersymmetric Spin(N) gauge theories with matter in the vector and spinor representations are considered. Dual descriptions are known for some of these theories. It is noted that when masses are given to all fields in the spinor representation, the dual gauge group G breaks to a group H such that \pi_2(G/H)=Z_2. The quantum numbers of the associated Z_2 monopole and those of the massive spinors are shown to agree, suggesting that the monopole is the image of the massive spinors under duality. It follows that electric sources in the spinor representation, needed as test charges to determine the phase of an SO(N) gauge theory, can be introduced as Z_2-valued magnetic sources in the dual nonabelian gauge theory. This fact is used to study the phases of SO(N) gauge theories with matter in the vector representation.

Global symmetries in duals of supersymmetric SU(N)×SU(M) and application to composite axion

In this paper, we construct a supersymmetric composite axion ( c-axion) model based on the gauge group SU( N)×SU( M), which is one possible physical application of the N=1 duality. The dual of SU( M) is interpreted as the color gauge group. We illustrate the existence of c-axion for the case of one dual quark in the dual gauge group SU ( M ̃ ) .

't Hooft conditions in supersymmetric dual theories

The matching of global anomalies of a supersymmetric gauge theory and its dual is seen to follow from similarities in their classical chiral rings. These similarities provide a formula for the dimension of the dual gauge group. As examples we derive 't Hooft consistency conditions for the duals of supersymmetric QCD and SU(N) theories with matter in the adjoint, and obtain the dimension of the dual groups.

Type IIA superstrings, chiral symmetry, and N = 1 4D gauge theory dualities

We study N = 1 four-dimensional gauge theories as the world-volume theory of D4-branes between NS 5-branes. We find constructions for a number of known field theory dualities involving SU( N c ) × SU( N′ c ) groups, coupled by matter fields F in the (N c, N − c) representation, in terms of branes of type IIA string theory. The dual gauge group follows from simply reversing the ordering of the NS 5-branes and the D6-branes while conserving magnetic charge on the world-volume of the branes. We interpret many field theory phenomena such as deformation of the superpotential W = Tr (F F ̃ ) k+1 in terms of the position of branes. By looking to D-branes for guidance, we find new N = 1 dualities involving arbitrary numbers of gauge groups. We propose a mechanism for enhanced chiral symmetry in the brane construction which, we conjecture, is associated with tensionless 3-branes in six dimensions.

More on chiral-nonchiral dual pairs

Expanding upon earlier work of Pouliot and Strassler, we construct chiral magnetic duals to nonchiral supersymmetric electric theories based upon SO(7), SO(8), and SO(9) gauge groups with various numbers of vector and spinor matter superfields. Anomalies are matched and gauge invariant operators are mapped within each dual pair. Renormalization group flows along flat directions are also examined. We find that confining phase quantum constraints in the electric theories are recovered from semiclassical equations of motion in their magnetic counterparts when the dual gauge groups are completely broken down by the Higgs mechanism.