Gauge Multiplet Research Articles

Dynamical generation of gauge and Higgs bosons in N = 2 supersymmetric non-linear sigma-models

A four-dimensional N = 2 supersymmetric non-linear sigma-model with the Eguchi-Hanson (ALE) target space and a non-vanishing central charge is rewritten to a classically equivalent and formally renormalizable gauged ‘linear’ sigma-model over a non-compact coset space in N = 2 harmonic superspace by making use of an N = 2 vector gauge superfield as the Lagrange multiplier. It is then demonstrated that the N = 2 vector gauge multiplet becomes dynamical after taking into account one-loop corrections due to quantized hypermultiplets. This implies the appearance of a composite gauge boson, a composite chiral spinor doublet and a composite complex Higgs particle, all defined as the physical states associated with the propagating N = 2 vector gauge superfield. The composite N = 2 vector multiplet is further identified with the zero-modes of a superstring ending on a D6-brane. Some non-perturbative phenomena, such as the gauge symmetry enhancement for coincident D6-branes and the Maldacena conjecture, turn out to be closely related to our NLSM via M-theory. Our results support a conjecture about the composite nature of superstrings ending on D-branes.

Large squark and slepton masses for the first-two generations in the anomalous U(1) SUSY breaking models

Considering that the soft SUSY breaking scalar masses come from a vacuum expectation value of the D-term for an external gauge multiplet, the renormalization of the scalar masses is related to the gauge anomaly. Then, if the external gauge symmetry is anomaly-free and has no kinetic mixing with the other U(1) gauge symmetries, the scalar masses are non-renormalized at all orders assuming that the gaugino masses are negligibly small compared with the scalar masses. Motivated by this, we construct models where the sfermion masses for the first-two generations are much heavier than the other superparticles in the minimal SUSY standard model in a framework of the anomalous U(1) mediated SUSY breaking. In these models we have to introduce extra chiral multiplets with the masses as large as those for the first-two generation sfermions. We find that phenomenologically desirable patterns for the soft SUSY breaking terms can be obtained in the models.

Gaugino mass without singlets

In models with dynamical supersymmetry breaking in the hidden sector, the gaugino masses in the observable sector have been believed to be extremely suppressed (below 1 keV), unless there is a gauge singlet in the hidden sector with specific couplings to the observable sector gauge multiplets. We point out that there is a pure supergravity contribution to gaugino masses at the quantum level arising from the superconformal anomaly. Our results are valid to all orders in perturbation theory and are related to the `exact' beta functions for soft terms. There is also an anomaly contribution to the A terms proportional to the beta function of the corresponding Yukawa coupling. The gaugino masses are proportional to the corresponding gauge beta functions, and so do not satisfy the usual GUT relations.

Classification of finite spectral triples

It is known that the spin structure on Riemannian manifold can be extended to noncommutative geometry using the notion of spectral triple. For finite geometries, the corresponding finite spectral triples are completely described in terms of matrices and classified using diagrams. When tensorized with the ordinary space-time geometry, finite spectral triples give rise to Yang-Mills theories with spontaneous symmetry breaking, whose characteristic features are given within the diagrammatic approach: vertices of the diagram correspond to gauge multiplets of chiral fermions and links to Yukawa couplings.

One-loop Pauli-Villars regularization of supergravity: Canonical gauge kinetic energy

It is shown that the one-loop coefficients of on-shell operators of standard supergravity with canonical gauge kinetic energy can be regulated by the introduction of Pauli-Villars chiral and Abelian gauge multiplets, subject to a condition on the matter representations of the gauge group. Aspects of the anomaly structure of these theories under global nonlinear symmetries and an anomalous gauge symmetry are discussed.

Supersymmetric models with product groups and field dependent gauge couplings

We study the dilaton-dependence of the effective action for N=1, SU(N1) x SU(N2) models with one generation of vectorlike matter transforming in the fundamental of both groups. We treat in detail the confining and Coulomb phases of these models writing explicit expressions in many cases for the effective superpotential. We can do so for the Wilson superpotentials of the Coulomb phase when N2=2, N1=2,4. In these cases the Coulomb phase involves a single U(1) gauge multiplet, for which we exhibit the gauge coupling in terms of the modulus of an elliptic curve. The SU(4) x SU(2) model reproduces the weak-coupling limits in a nontrivial way. In the confining phase of all of these models, the dilaton superpotential has a runaway form, but in the Coulomb phase the dilaton enjoys flat directions. Had we used the standard moduli-space variables: Tr M^k, k=1,..., N2, with M the quark condensate matrix, to parameterize the flat directions instead of the eigenvalues of M, we would find physically unacceptable behaviour, illustrating the importance to correctly identify the moduli.

Invariant Regularization of Supersymmetric Chiral Gauge Theory

We formulate a manifestly supersymmetric gauge covariant regularization of supersymmetric chiral gauge theories. In our scheme, the effective action in the superfield background field method above one-loop is always supersymmetric and gauge invariant. The gauge anomaly has a covariant form and can emerge only in one-loop diagrams with all the external lines being the background gauge superfield. We also present several illustrative applications in the one-loop approximation: the self-energy part of the chiral multiplet and of the gauge multiplet; the super-chiral anomaly and the superconformal anomaly; as the corresponding anomalous commutators, the Konishi anomaly and an anomalous supersymmetric transformation law of the supercurrent (the “central extension” of N=1 supersymmetry algebra) and of the R-current.

Nonholomorphic N=2 terms in N=4 super Yang-Mills theory: 1-loop calculation in N=2 superspace

The effective action of N=2 gauge multiplets in general includes higher-dimension UV finite nonholomorphic corrections integrated with the full N=2 superspace measure. By adding a hypermultiplet in the adjoint representation we study the effective action of N=4 super Yang-Mills theory. The nonanomalous SU(4) R-symmetry of the classical N=4 theory must also be present in the on-shell effective action, and therefore we expect to find similar nonholomorphic terms for each of the scalars in the hypermultiplet. The N=2 path integral quantization formalism developed in projective superspace allows us to compute these hypermultiplet nonholomorphic terms directly in N=2 superspace. The corresponding gauge multiplet expression can be successfully compared with the result inferred from a N=1 calculation in the abelian subsector.

On non-linear superfield versions of the vector-tensor multiplet

We propose a harmonic superspace description of the non-linear vector-tensor N=2 multiplet. We show that there exist two inequivalent version: the old one in which one of the vectors is the field-strength of a gauge two-form, and a new one in which this vector satisfies a non-linear constraint and cannot be expressed in terms of a potential. In this the new version resembles the non-linear N=2 multiplet. We perform the dualization of both non-linear versions and discuss the resulting K\"ahler potentials. Finally, we couple the non-linear vector-tensor multiplet to an abelian background gauge multiplet.

Calogero-Moser systems in SU( N) Seiberg-Witten theory

The Seiberg-Witten curve and differential for N = 2 supersymmetric SU( N) gauge theory, with a massive hypermultiplet in the adjoint representation of the gauge group, are analyzed in terms of the elliptic Calogero-Moser integrable system. A new parametrization for the Calogero-Moser spectral curves is found, which exhibits the classical vacuum expectation values of the scalar field of the gauge multiplet. The one-loop perturbative correction to the effective prepotential is evaluated explicitly, and found to agree with quantum field theory predictions. A renormalization group equation for the variation with respect to the coupling is derived for the effective prepotential, and may be evaluated in a weak-coupling series using residue methods only. This gives a simple and efficient algorithm for the instanton corrections to the effective prepotential to any order. The one- and two-instanton corrections are derived explicitly. Finally, it is shown that certain decoupling limits yield N = 2 supersymmetric theories for simple gauge groups SU( N 1) with hypermultiplets in the fundamental representation, while others yield theories for product gauge groups SU( N 1) ×…× SU( N p ), with hypermultiplets in fundamental and bi-fundamental representations. The spectral curves obtained this way for these models agree with the ones proposed by Witten using D-branes and M-theory.

Supergravity with gauged second order symmetry

A D = 4, N = 1 supergravity model is presented which unites, through a continuous deformation parameter, new minimal supergravity with an extra U (1) gauge multiplet and standard supergravity with local R -symmetry in a formulation with a nonstandard set of auxiliary fields. The deformation gauges a second order symmetry, implements an electromagnetic duality relating the extra U (1) to the R -symmetry, and breaks supersymmetry spontaneously.

The tensor Goldstone multiplet for partially broken supersymmetry

We show that the tensor gauge multiplet of N = 1 supersymmetry can serve as the Goldstone multiplet for partially broken rigid N = 2 supersymmetry. We exploit a remarkable analogy with the Goldstone-Maxwell multiplet of [1] to find its nonlinear transformation law and its invariant Goldstone action. We demonstrate that the tensor multiplet has two dualities. The first transforms it into the chiral Goldstone multiplet; the other leaves it invariant.

Local BRST Cohomology in MinimalD=4,N=1 Supergravity

The local BRST cohomology is computed in old and new minimal supergravity, including the coupling to Yang–Mills gauge multiplets. This covers the determination of all gauge invariant local actions for these models, the classification of all the possible counterterms that are invariant on-shell, of all candidate gauge anomalies, and of the possible nontrivial (continuous) deformations of the standard actions and gauge transformations. Among others it is proved that in old minimal supergravity the most general gauge invariant action can indeed be constructed from well-known superspace integrals, whereas in new minimal supergravity there are only a few additional (but important) contributions which cannot be constructed in this way without further ado. Furthermore the results indicate that supersymmetry itself is not anomalous in minimal supergravity and show that the gauge transformations are extremely stable under consistent deformations of the models. There is, however, an unusual deformation converting new into old minimal supergravity with localR-invariance which is reminiscent of a duality transformation.

Unification bounds on the possible N = 2 supersymmetry-breaking scale

In this letter, the possible appearance of N=2 supersymmetry at a low energy scale is investigated in the context of unified theories. Introducing mirror particles for all the gauge and matter multiplets of the Minimal Supersymmetric extension of the Standard Model (MSSM), the measured values of sin^2 \theta_W and \alpha_3(M_Z) indicate that the N=2 threshold scale M_{S_2} cannot be lower than \sim 10^{14}GeV. If the U(1) normalization coefficient k is treated as a free parameter, M_{S_2} can be as low as 10^9 GeV. On the other hand, if mirror quarks and leptons are absent and a non-standard value for k is used, N=2 supersymmetry breaking could in principle occur at the electroweak scale.

Curves of marginal stability, and weak- and strong-coupling BPS spectra in N = 2 supersymmetric QCD

We explicitly determine the global structure of the SL(2, Z ) bundle over the Coulomb branch of the moduli space of asymptotically free N = 2 supersymmetric Yang-Mills theories with gauge group SU(2) when massless hypermultiplets are present. For each relevant number of flavours, we show that there is a curve of marginal stability of the Coulomb branch, diffeomorphic to a circle, across which the BPS spectrum is discontinuous. We determine rigorously and completely the BPS spectra inside and outside the curve. In all cases, the spectrum inside the curve consists of only those BPS states that are responsible for the singularities of the low energy effective action (in addition to the massless abelian gauge multiplet which is always present). The predicted decay patterns across the curve of marginal stability are perfectly consistent with all quantum numbers carried by the BPS states. As a byproduct, we also show that the electric and magnetic quantum numbers of the massless states at the singularities proposed by Seiberg and Witten are the only possible ones.

New Approach to the U(2,2)-Symmetry in Spinor and Gravitation Theory

Generally-relativistic Dirac equation is reinterpreted as an approximation to the more fundamental model based on the quadruplet of Klein-Gordon particles with the internal hermitian metric of the neutral signature (++−−). Compensating field of the local group U(2,2) of internal symmetries splits under the GL(2, C)-reduction into gravitational co-tetrad, Einstein-Cartan-Weyl affine connection, and an auxiliary co-tetrad-like object. Equation for the matter field shows under the SL(2,C)-reduction a reasonable correspondence with the generally relativistic Dirac theory. Masses of fermions may be dynamically generated by non vanishing “vacuum” values of geometrodynamical quantities. There is also a convincing correspondence between Yang-Mills equations for the U(2,2)-gauge field and the Einstein-Cartan theory, or more general metric-affine theories of gravitation. In our approach the tetrad field is neither a reference frame nor a compensating field of translations in originally Minkowskian space, but a part of the U(2,2)-gauge multiplet.

Gauged hyperinstantons and monopole equations

The monopole equations in the dual abelian theory of the N = 2 gauge-theory, recently proposed by Witten as a new tool to study topological invariants, are shown to be the simplest elements in a class of instanton equations that follow from the improved topological twist mechanism introduced by the authors in previous papers. When applied to the N = 2 σ-model, this twisting procedure suggested the introduction of the so-called hyperinstantons that are the solutions to an appropriate condition of triholomorphicity imposed on the maps q: m → n from a four-dimensional almost quaternionic world-manifold m to an almost quaternionic target manifold n . When gauging the σ-model by coupling it to the vector multiplet of a gauge group G, one gets instantonic conditions (named by us gauged hyperinstantons) that reduce to the Seiberg-Witten equations for > m = n = R 4 and G = U(1). The deformation of the self-duality condition on the gauge-field strength due to the monopole-hyperinstanton is very similar to the deformation of the self-duality condition on the Riemann curvature previously observed by the authors when the hyperinstantons are coupled to topological gravity. In this paper the general form of the hyperinstantonic equations coupled to both gravity and gauge multiplets is presented.

The nonlinear multiplet revisited

Using a reformulation of the nonlinear multiplet as a gauge multiplet, we discuss its dynamics. We show that the nonlinear “duality” that appears to relate the model to a conventional σ-model introduces a new sector into the theory.

Pauli-Villars regularization of supergravity coupled to chiral and Yang-Mills matter

It is shown that the one-loop quadratic divergences of standard supergravity can be regulated by the introduction of heavy Pauli-Villars fields belonging to chiral and abelian gauge multiplets. The resulting one-loop correction can be interpreted as a renormalization of the Kähler potential. Regularization of the dilaton couplings to the Yang-Mills sector requires special care, and may shed some light on chiral/linear multiplet duality of the dilaton supermultiplet.

Generalized On-Shell Ward Identities in String Theory

It is demonstrated that an infinite set of string-tree level on-shell Ward identities, which are valid to all sigma-model loop orders, can be systematically constructed without referring to the string field theory. As examples, bosonic massive scattering amplitudes are calculated explicitly up to the second massive excited states. Ward identities satisfied by these amplitudees are derived by using zero-norm states in the spetrum. In particular, the inter-particle Ward identity generated by the D2xD2' zero-norm state at the second massive level is demonstrated. The four physical propagating states of this mass level are then shown to form a large gauge multiplet. This result justifies our previous consideration on higher inter-spin symmetry from the generalized worldsheet sigma-model point of view.