Arbitrary Gauge Group Research Articles

Electrically gauged $ \mathcal{N}=4 $ supergravities in D = 4 with $ \mathcal{N}=2 $ vacua

We study $ \mathcal{N}=2 $ vacua in spontaneously broken $ \mathcal{N}=4 $ electrically gauged supergravities in four space-time dimensions. We argue that the classification of all such solutions amounts to solving a system of purely algebraic equations. We then explicitly construct a special class of consistent $ \mathcal{N}=2 $ solutions and study their properties. In particular we find that the spectrum assembles in $ \mathcal{N}=2 $ massless or BPS supermultiplets. We show that (modulo U(1) factors) arbitrary unbroken gauge groups can be realized provided that the number of $ \mathcal{N}=4 $ vector multiplets is large enough. Below the scale of partial supersymmetry breaking we calculate the relevant terms of the low-energy effective action and argue that the special Kähler manifold for vector multiplets is completely determined, up to its dimension, and lies in the unique series of special Kähler product manifolds.

Self-dual Yang-Mills and vector-spinor fields, nilpotent fermionic symmetry, and supersymmetric integrable systems

We present a system of a self-dual Yang-Mills field and a self-dual vector-spinor field with nilpotent fermionic symmetry (but not supersymmetry) in $2+2$ dimensions, that generates supersymmetric integrable systems in lower dimensions. Our field content is $(A_{\ensuremath{\mu}}{}^{I},\ensuremath{\psi}_{\ensuremath{\mu}}{}^{I},{\ensuremath{\chi}}^{IJ})$, where $I$ is the adjoint index of arbitrary gauge group. The ${\ensuremath{\chi}}^{IJ}$ is a Stueckelberg field for consistency. The system has local nilpotent fermionic symmetry with the algebra ${N_{\ensuremath{\alpha}}{}^{I},N_{\ensuremath{\beta}}{}^{J}}=0$. This system generates supersymmetric Kadomtsev-Petviashvili equations in $D=2+1$, and supersymmetric Korteweg--de Vries equations in $D=1+1$ after appropriate dimensional reductions. We also show that a similar self-dual system in seven dimensions generates a self-dual system in four dimensions. Based on our results we conjecture that lower-dimensional supersymmetric integral models can be generated by nonsupersymmetric self-dual systems in higher dimensions only with nilpotent fermionic symmetries.

Computing theθ-exact Seiberg-Witten map for arbitrary gauge groups

We discuss how to obtain \theta-exact Seiberg-Witten maps by expanding in the gauge coupling constant or, equivalently, in the number of ordinary gauge fields. We do so for arbitrary compact gauge groups in arbitrary unitary representations. For gauge and matter fields, we fully work out \theta-exact non-hybrid Seiberg-Witten maps up to order three in the number of ordinary gauge fields.

Calculating the renormalisation group equations of a SUSY model with Susyno

Susyno is a Mathematica package dedicated to the computation of the 2-loop renormalisation group equations of a supersymmetric model based on any gauge group (the only exception being multiple U(1) groups) and for any field content.Program summaryProgram title: SusynoCatalogue identifier: AEMX_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEMX_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 30829No. of bytes in distributed program, including test data, etc.: 650170Distribution format: tar.gzProgramming language: Mathematica 7 or higher.Computer: All systems that Mathematica 7+ is available for (PC, Mac).Operating system: Any platform supporting Mathematica 7+ (Windows, Linux, Mac OS).Classification: 4.2, 5, 11.1.Nature of problem:Calculating the renormalisation group equations of a supersymmetric model involves using long and complicated general formulae [1, 2]. In addition, to apply them it is necessary to know the Lagrangian in its full form. Building the complete Lagrangian of models with small representations of SU(2) and SU(3) might be easy but in the general case of arbitrary representations of an arbitrary gauge group, this task can be hard, lengthy and error prone.Solution method:The Susyno package uses group theoretical functions to calculate the super-potential and the soft-SUSY-breaking Lagrangian of a supersymmetric model, and calculates the two-loop RGEs of the model using the general equations of [1, 2]. Susyno works for models based on any representation(s) of any gauge group (the only exception being multiple U(1) groups).Restrictions:As the program is based on the formalism of [1, 2], it shares its limitations. Running time can also be a significant restriction, in particular for models with many fields.Unusual features:Susyno contains functions that (a) calculate the Lagrangian of supersymmetric models and (b) calculate some group theoretical quantities. Some of these functions are available to the user and can be freely used. A built-in help system provides detailed information.Running time:Tests were made using a computer with an Intel Core i5 760 CPU, running under Ubuntu 11.04 and with Mathematica 8.0.1 installed. Using the option to suppress printing, the one- and two-loop beta functions of the MSSM were obtained in 2.5 s (NMSSM: 5.4 s). Note that the running time scales up very quickly with the total number of fields in the model.

On the solutions of generalized Bogomolny equations

Generalized Bogomolny equations are encountered in the localization of the topological N=4 SYM theory. The boundary conditions for 't Hooft and surface operators are formulated by giving a model solution with some special singularity. In this note we consider the generalized Bogomolny equations on a half space and construct model solutions for the boundary 't Hooft and surface operators. It is shown that for the 't Hooft operator the equations reduce to the open Toda chain for arbitrary simple gauge group. For the surface operators the solutions of interest are rational solutions of a periodic non-abelian Toda system.

The ABCDEFG of instantons and W-algebras

For arbitrary gauge groups, we check at the one-instanton level that the Nekrasov partition function of pure N=2 super Yang-Mills is equal to the norm of a certain coherent state of the corresponding W-algebra. For non-simply-laced gauge groups, we confirm in particular that the coherent state is in the twisted sector of a simply-laced W-algebra.

On the instantons and the hypermultiplet mass of $ \mathcal{N} = {{2}^{ * }} $ super Yang-Mills on S 4

We show that the physical N=4 super Yang-Mills theory on a four-sphere with an arbitrary gauge group receives no instanton contributions, by clarifying the relation between the hypermultiplet mass and the equivariant parameters of the mass-deformed theory preserving N=2 supersymmetry. The correct relation also implies that N=4 superconformal Yang-Mills theory with gauge group SU(2) corresponds to Liouville theory on a torus with the insertion of a non-trivial operator, rather than the identity as have been claimed in the literature.

’t Hooft operators in the boundary

We consider a topologically twisted maximally supersymmetric Yang-Mills theory on a four-manifold of the form $V = W \times {\mathbb R}_+$. 't Hooft disorder operators localized in the boundary component at finite distance of $V$ are relevant for the study of knot theory on the three-manifold $W$, and have recently been constructed for a gauge group of rank one. We extend this construction to an arbitrary gauge group $G$. For certain values of the magnetic charge of the 't Hooft operator, the solutions are obtained by embedding the rank one solutions in $G$ and can be given in closed form.

On quasi-local charges and Newman–Penrose type quantities in Yang–Mills theories

We generalize the notion of quasi-local charges, introduced by P Tod for Yang–Mills fields with unitary gauge groups, to non-Abelian gauge theories with arbitrary gauge groups, and calculate its small sphere and large sphere limits both at spatial and null infinity. We show that for semisimple gauge groups no reasonable definition yield conserved total charges and Newman–Penrose (NP) type quantities at null infinity in generic, radiative configurations. The conditions of their conservation, both in terms of the field configurations and the structure of the gauge group, are clarified. We also calculate the NP quantities for stationary, asymptotic solutions of the field equations with vanishing magnetic charges, and illustrate these by explicit solutions with various gauge groups.

SEIBERG–WITTEN EQUATIONS FROM FEDOSOV DEFORMATION QUANTIZATION OF ENDOMORPHISM BUNDLE

It is shown how Seiberg–Witten equations can be obtained by means of Fedosov deformation quantization of endomorphism bundle and the corresponding theory of equivalences of star products. In such setting, Seiberg–Witten map can be iteratively computed for arbitrary gauge group up to any given degree with recursive methods of Fedosov construction. Presented approach can be also considered as a generalization of Seiberg–Witten equations to Fedosov type of noncommutativity.

On the gauge orbit types for theories with classical compact gauge group

We classify principal O( n )-bundles over 4-dimensional closed manifolds for n = 3 and n ≥ 5 and SO(2 n )-bundles over 2 n -dimensional closed manifolds. This is part of a program to determine the orbit types of the action of the group of local gauge transformations on gauge potentials for an arbitrary compact classical gauge group and an arbitrary 4-dimensional space-time.

Duality-symmetric supersymmetric Yang-Mills theory in three dimensions

We formulate a duality-symmetric $N=1$ supersymmetric Yang-Mills theory in three dimensions. Our field content is $(A_{\ensuremath{\mu}}{}^{I},{\ensuremath{\lambda}}^{I},{\ensuremath{\varphi}}^{I})$, where the index $I$ is for the adjoint representation of an arbitrary gauge group $G$. Our Hodge duality symmetry is $F_{\ensuremath{\mu}\ensuremath{\nu}}{}^{I}=+ϵ_{\ensuremath{\mu}\ensuremath{\nu}}{}^{\ensuremath{\rho}}{D}_{\ensuremath{\rho}}{\ensuremath{\varphi}}^{I}$. Because of this relationship, the presence of two physical fields $A_{\ensuremath{\mu}}{}^{I}$ and ${\ensuremath{\varphi}}^{I}$ within the same $N=1$ supermultiplet poses no problem. We can couple this multiplet to another vector multiplet $(C_{\ensuremath{\mu}}{}^{I},{\ensuremath{\chi}}^{I};B_{\ensuremath{\mu}\ensuremath{\nu}}{}^{I})$ with $1+1$ physical degrees of freedom modulo $\mathrm{dim}\text{ }G$. Thanks to peculiar couplings and supersymmetry, the usual problem with an extra vector field in a nontrivial representation does not arise in our system.

Supersymmetric [formula omitted] gauge theory with arbitrary gauge group

A new universal model to implement the Seiberg–Witten approach to low-energy properties of the supersymmetric N = 2 gauge theory with an arbitrary compact simple gauge group, classical or exceptional, is suggested. It is based on the hyperelliptic curve, whose genus equals the rank of the gauge group. The weak and strong coupling limits are reproduced. The magnetic and electric charges of light dyons, which are present in the proposed model comply with recent predictions derived from the general properties of the theory. The discrete chiral symmetry is implemented, the duality condition is reproduced, and connections between monodromies at weak and strong coupling are established. It is found that the spectra of monopoles and dyons are greatly simplified when vectors representing the scalar and dual fields in the Cartan algebra are aligned along the Weyl vector. This general feature of the theory is used for an additional verification of the model. The model predicts the identical analytic structures of the coupling constants for the theories based on the SU ( r + 1 ) and Sp ( 2 r ) gauge groups.

Multiplicative bundle gerbes with connection

Multiplicative bundle gerbes are gerbes over a Lie group which are compatible with the group structure. In this article connections on such bundle gerbes are introduced and studied. It is shown that multiplicative bundle gerbes with connection furnish geometrical constructions of the following objects: smooth central extensions of loop groups, Chern–Simons actions for arbitrary gauge groups, and symmetric bi-branes for WZW models with topological defect lines.

S-duality, 't Hooft operators and the operator product expansion

We study S-duality in N=4 super Yang-Mills with an arbitrary gauge group by determining the operator product expansion of the circular BPS Wilson and 't Hooft loop operators. The coefficients in the expansion of an 't Hooft loop operator for chiral primary operators and the stress-energy tensor are calculated in perturbation theory using the quantum path-integral definition of the 't Hooft operator recently proposed. The corresponding operator product coefficients for the dual Wilson loop operator are determined in the strong coupling expansion. The results for the 't Hooft operator in the weak coupling expansion exactly reproduce those for the dual Wilson loop operator in the strong coupling expansion, thereby demonstrating the quantitative prediction of S-duality for these observables.

Constructing Non-Abelian Vortices with Arbitrary Gauge Groups

Constructing Non-Abelian Vortices with Arbitrary Gauge Groups

Hitchin's equations and integrability of BPSZNstrings in Yang-Mills theories

We show that ZN string's BPS equations are equivalent to the Hitchin's equations (or self-duality equation) and also to the zero curvature condition. We construct the general form for BPS ZN string solutions for arbitrary simple gauge groups with non-trivial center. Depending on the vacuum solutions considered, the ZN string's BPS equations reduce to different two dimensional integrable field equations. For a particular vacuum we obtain the equation of affine Toda field theory.

Sparticle masses in Higgsed gauge mediation

We generalize the gauge sector of gauge-mediated supersymmetry breaking to allow for an arbitrary gauge group with an arbitrary supersymmetric Higgsing. The sparticle masses are computed to leading order in the gauge coupling. The generic effect on the MSSM spectrum from additional Higgsed gauge structure is to increase the sfermion masses relative to the gaugino masses.

On relating multiple M2 and D2-branes

Due to the difficulties of finding superconformal Lagrangian theories for multiple M2-branes, we will in this paper instead focus on the field equations. By relaxing the requirement of a Lagrangian formulation we can explore the possibility of having structure constants $f^{ABC}{}_D$ satisfying the fundamental identity but which are not totally antisymmetric. We exemplify this discussion by making use of an explicit choice of a non-antisymmetric $f^{ABC}{}_D$ constructed from the Lie algebra structure constants $f^{ab}{}_c$ of an arbitrary gauge group. Although this choice of $f^{ABC}{}_D$ does not admit an obvious Lagrangian description, it does reproduce the correct SYM theory for a stack of $N$ D2-branes to leading order in $g_{YM}^{-1}$ upon reduction and, moreover, it sheds new light on the centre of mass coordinates for multiple M2-branes.

Constructing non-Abelian vortices with arbitrary gauge groups

We construct the general vortex solution in the color–flavor-locked vacuum of a non-Abelian gauge theory, where the gauge group is taken to be the product of an arbitrary simple group and U(1). Use of the holomorphic invariants allows us to extend the moduli-matrix method and to determine the vortex moduli space in all cases. Our approach provides a new framework for studying solitons of non-Abelian varieties with various possible applications in physics.