Arbitrary Gauge Group Research Articles

Non-holomorphic effective potential in N=4 SU( n) SYM

We compute the one-loop non-holomorphic effective potential for the N=4 SU( n) supersymmetric Yang-Mills theory with the gauge symmetry broken down to the maximal torus U(1) n−1 . Our approach remains powerful for arbitrary gauge groups and is based on the use of N=2 harmonic superspace formulation for general N=2 Yang-Mills theories along with the superfield background field method.

Three-dimensional N = 2 gauge theories and degenerations of Calabi-Yau four-folds

Three-dimensional N = 2 gauge theories with arbitrary gauge group and fundamental flavors are engineered from degenerations of Calabi-Yau four-folds. We show how Coulomb and Higgs branches emerge in the geometric picture. The analysis of instanton generated superpotentials unravels interesting aspects of the five-brane effective action in M-theory.

On the spontaneous identity of chiral and supersymmetry breaking in pure super Yang-Mills theories

We show that in supersymmetric pure Yang-Mills theories with arbitrary simple gauge group, the spontaneous breaking of chiral fermionic and bosonic charge by the associated gaugino and gauge boson condensates implies the spontaneous breaking of supersymmetry by the condensate of the underlying Lagrangian density. The explicit breaking of the restricted fermionic charge through the chiral anomaly is deferred to a secondary stage in the elimination of infrared singularities or long range forces.

Canθ/Ndependence for gluodynamics be compatible with2πperiodicity inθ?

In a number of field theoretical models the vacuum angle \theta enters physics in the combination \theta/N, where N stands generically for the number of colors or flavors, in an apparent contradiction with the expected 2 \pi periodicity in \theta. We argue that a resolution of this puzzle is related to the existence of a number of different \theta dependent sectors in a finite volume formulation, which can not be seen in the naive thermodynamic limit V -> \infty. It is shown that, when the limit V -> \infty is properly defined, physics is always 2 \pi periodic in \theta for any integer, and even rational, values of N, with vacuum doubling at certain values of \theta. We demonstrate this phenomenon in both the multi-flavor Schwinger model with the bosonization technique, and four-dimensional gluodynamics with the effective Lagrangian method. The proposed mechanism works for an arbitrary gauge group.

A non-perturbative non-renormalization theorem for the Wilsonian gauge couplings in supersymmetric theories

We show that the holomorphic Wilsonian beta-function of a renormalizable asymptotically free supersymmetric gauge theory with an arbitrary semi-simple gauge group, matter content, and renormalizable superpotential is exhausted at 1-loop with no higher loops and no non-perturbative contributions. This is a non-perturbative extension of the well known result of Shifman and Vainshtein.

Instantons and magnetic monopoles on R3×S1 with arbitrary simple gauge groups

We investigate Yang-Mills theories with arbitrary gauge group on R3×S1, whose symmetry is spontaneously broken by the Wilson loop. We show that instantons are made of fundamental magnetic monopoles, each of which has a corresponding root in the extended Dynkin diagram. The number of constituent magnetic monopoles for a single instanton is the dual Coxeter number of the gauge group, which also accounts for the number of instanton zero modes. In addition, we show that there exists a novel type of the S1 coordinate dependent magnetic monopole solutions in G2,F4,E8.

Dynamics of Bogomol’nyi-Prasad-Sommerfield dyons: Effective field theory approach

Based on a detailed analysis of nonlinear field equations of the SU(2) Yang-Mills-Higgs system, we obtain the effective field theory describing low-energy interaction of BPS dyons and massless particles (i.e., photons and Higgs particles). Our effective theory manifests electromagnetic duality and spontaneously broken scale symmetry, and reproduces the multimonopole moduli space dynamics of Manton in a suitable limit. Also given is a generalization of our approach to the case of BPS dyons in a gauge theory with an arbitrary gauge group that is maximally broken.

Dyon electric charge and fermion fractionalization in N = 2 gauge theory

A first principles calculation of the quantum corrections to the electric charge of a dyon in an N = 2 gauge theory with arbitrary gauge group is presented. These corrections arise from the fermion fields via the mechanism of fermion fractionalization. For a dyon whose magnetic charge is a non-simple co-root, the correction is a discontinuous function on the moduli space of vacua and the discontinuities occur precisely on co-dimension-I curves on which the dyon decays. In this way, the complete spectrum of dyons at weak coupling is found for a theory with any gauge group. It is shown how this spectrum is consistent with the semi-classical monodromies.

Solutions of extended supersymmetric matrix models for arbitrary gauge groups

Energy eigenstates for N=2 supersymmetric gauged quantum mechanics are found for the gauges groups SU(n) and U(n). The analysis is aided by the existence of an infinite number of conserved operators. The spectum is continuous. Perturbative eigenstates for $N>2$ are also presented, a case which is relevant for the conjectured description of M theory in the infinite momentum frame.

Dynamics of N = 2 supersymmetric gauge theories in three dimensions

We study the structure of the moduli spaces of vacua and superpotentials of N = 2 supersymmetric gauge theories in three dimensions. By analyzing the instanton corrections, we compute the exact superpotentials and determine the quantum Coulomb and Higgs branches of the theories in the weak coupling regions. We find candidates for non-trivial N = 2 superconformal field theories at the singularities of the moduli spaces. The analysis is carried out explicitly for gauge groups U( N c ) and SU( N c ) with N f flavors. We show that the field theory results are in complete agreement with the intersecting branes picture. We also compute the exact superpotentials for arbitrary gauge groups and arbitrary matter content.

Semi-classical quantization in N = 4 supersymmetric Yang-Mills theory and duality

At a generic point in the moduli space of vacua of an N = 4 supersymmetric gauge theory with arbitrary gauge group the Higgs force does not cancel the magneto-static force between magnetic monopoles of distinct charge. As a consequence the moduli space of magnetically charged solutions is related in a simple way to those of the SU(2) theory. This leads to a rather simple test of S-duality. On certain subspaces of the moduli space of vacua the forces between distinct monopoles cancel and the test of S-duality becomes more complicated.

Modular invariant formulation of multi-gaugino and matter condensation

Using the linear multiplet formulation for the dilaton superfield, we construct an effective Lagrangian for hidden sector gaugino condensation in string effective field theories with arbitrary gauge groups and matter. Non-perturbative string corrections to the Kähler potential are invoked to stabilize the dilaton at a supersymmetry breaking minimum of the potential. When the cosmological constant is tuned to zero the moduli are stabilized at their self-dual points, and the vevs of their F-component superpartners vanish. Numerical analyses of one- and two-condensate examples with massless chiral matter show considerable enhancement of the gauge hierarchy with respect to the E 8 case. The non-perturbative string effects required for dilaton stabilization may have implications for gauge coupling unification. As a comparison, we also consider a parallel approach based on the commonly used chiral formulation.

Spontaneous N = 2 → N = 1 local supersymmetry breaking with surviving compact gauge groups

Generic partial supersymmetry breaking of N = 2 supergravity with zero vacuum energy and with surviving unbroken arbitrary gauge groups is exhibited. Specific examples are given.

N = 2 curves and a Coulomb phase in N = 1 SUSY gauge theories with adjoint and fundamental matters

We study low-energy effective superpotentials for the phase with a confined photon in N=1 supersymmetric gauge theories with an adjoint matter $\Phi$ and fundamental flavors $Q, \tilde Q$. Arbitrary classical gauge groups are considered. The results are used to derive the hyperelliptic curves which describe the Coulomb phase of N=2 supersymmetric QCD with classical gauge groups. These curves are in agreement with those proposed earlier by several authors. Our results also produce the curves relevant to describe the Coulomb phase of N=1 theories with a superpotential of the form $\tilde{Q} \Phi^{l} Q$.

Coordinate-free quantization of first-class constrained systems

The coordinate-free formulation of canonical quantization, achieved by a flat-space Brownian motion regularization of phase-space path integrals, is extended to a special class of closed first-class constrained systems that is broad enough to include Yang-Mills type theories with an arbitrary compact gauge group. Central to this extension are the use of coherent state path integrals and of Lagrange multiplier integrations that engender projection operators onto the subspace of gauge invariant states.

EXACT SOLUTIONS OF THE REISSNER–NORDSTRÖM TYPE IN EINSTEIN–YANG–MILLS SYSTEMS WITH ARBITRARY GAUGE GROUPS AND SPACE–TIME DIMENSIONS

We present a class of solutions in Einstein–Yang–Mills systems with arbitrary gauge groups and space–time dimensions, which are symmetric under the action of the group of spatial rotations. Our approach is based on the dimensional reduction method for gauge and gravitational fields and relates symmetric Einstein–Yang–Mills solutions to certain solutions of two-dimensional Einstein–Yang–Mills–Higgs-dilaton theory. Application of this method to four-dimensional spherically symmetric (pseudo-)Riemannian space–time yields, in particular, new solutions describing both a magnetic and an electric charge at the center of a black hole. Moreover, we give an example of a solution with non-Abelian gauge group in six-dimensional space–time. We also comment on the stability of the obtained solutions.

S-duality in N = 4 supersymmetric gauge theories with arbitrary gauge group

The Goddard, Nuyts and Olive conjecture for electric-magnetic duality in Yang-Mills theory with an arbitrary gauge group G is extended by including a non-vanishing vacuum angle θ. This extended S-duality conjecture includes the case when the unbroken gauge group is non-abelian and a definite prediction for the spectrum of dyons results.

Moduli space of many BPS monopoles for arbitrary gauge groups.

We study the moduli space for an arbitrary number of BPS monopoles in a gauge theory with an arbitrary gauge group that is maximally broken to $U(1)^k$. From the low energy dynamics of well-separated dyons we infer the asymptotic form of the metric for the moduli space. For a pair of distinct fundamental monopoles, the space thus obtained is $R^3 \times(R^1\times {\cal M}_0)/Z$ where ${\cal M}_0$ is the Euclidean Taub-NUT manifold. Following the methods of Atiyah and Hitchin, we demonstrate that this is actually the exact moduli space for this case. For any number of such objects, we show that the asymptotic form remains nonsingular for all values of the intermonopole distances and that it has the symmetries and other characteristics required of the exact metric. We therefore conjecture that the asymptotic form is exact for these cases also.

Heterotic gauge structure of type II K3 fibrations

We show that certain classes of K3 fibered Calabi-Yau manifolds derive from orbifolds of global products of K3 surfaces and particular types of curves. This observation explains why the gauge groups of the heterotic duals are determined by the structure of a single K3 surface and provides the dual heterotic picture of conifold transitions between K3 fibrations. Abstracting our construction from the special case of K3 hypersurfaces to general K3 manifolds with an appropriate automorphism, we show how to construct Calabi-Yau threefold duals for heterotic theories with arbitrary perturbative gauge groups. This generalization reveals that the previous limit on the Euler number of Calabi-Yau manifolds is an artifact of the restriction to the framework of hypersurfaces.

Electromagnetic duality and SU(3) monopoles

We consider the low-energy dynamics of a pair of distinct fundamental monopoles that arise in the N = 4 supersymmetric SU(93) Yang-Mills theory broken to U(1) × U(1). Both the long distance interactions and the short distance behavior indicate that the moduli space is R 3 × (R 1 × M 0) Z where M 0 is the smooth Taub-NUT manifold, and we confirm this rigorously. By examining harmonic forms on the moduli space, we find a threshold bound state of two monopoles with a tower of BPS dyonic states built on it, as required by Montonen-Olive duality. We also present a conjecture for the metric of the moduli space for any number of distinct fundamental monopoles for an arbitrary gauge group.