Superstring propagation in curved superspace in the presence of background super Yang-Mills fields

A gauge invariant action is presented which describes the propagation of the superstring in curved superspace in the presence of background super Yang-Mills fields. It is shown that this action posseses the local fermionic world-sheet symmetry needed for a consistent coupling of the string to background fields. Some other aspects of the superspace non-linear σ-model described by this action are also discussed.     

Light-cone auxiliary fields for ten-dimensional super Yang-Mills

We consider ten-dimensional super Yang-Mills in the light-cone gauge and define a set of auxiliary fields which close the light-cone super algebra off-shell. As a necessary preliminary we give a systematic discussion of the auxiliary field problem for simple super Yang-Mills in dimensions 3, 4, 6 and 10 both covariantly and in the light-cone framework. The motivation for this work is that it may prove useful in conjunction with the ideas of harmonic superspace. With this in mind we indicate how the light-cone theory in ten dimensions can be formulated in light-cone superspace using unconstrained superfields.     

Self-duality in superspace

The absence of local divergences in the vacuum functional of supergravity at all loop orders in a self-dual gravitational or supergravitational background is discussed. It is also shown that the first variational derivative of the generating functional of supergravity has no gauge independent divergences in a self-dual background, in particular that the gauge independent part of the energy momentum tensor is finite in a self-dual background. Simple expressions defining the corresponding half-flat superspace are presented.     

The Witten index in superspace,two-dimensional superanomaly in Yang-Mills and gravitational background,and superspace Schwinger-Dewitt heat kernel method

We consider the Witten index in superspace and show that it is closely related to the superspace Schwinger-DeWitt heat kernel. By evaluating the Witten index for the two-dimensional superspace Yang-Mills and gravitational systems we obtain the two-dimensional superanomaly in an efficient way. Furthermore we show an effective way to treat the three-dimensional supersymmetric Yang-Mills system by the superspace Schwinger-DeWitt heat kernel method. As a consequence, the supersymmetric Chern-Simons term is obtained.     

Conformal symmetry breaking and mass generation

We consider an extension of the supersymmetry formalism in order to include gauge fields. We construct a fiber bundle P(M ₄×{θ}, G) over the superspace with the gauge group as the structural group. We obtain the equations of interacting pure Yang-Mills and massless Higgs fields, considering these fields as the components of the same gauge field. Moreover, by fixing a gauge we generate a mass as a result of the supersymmetry breaking. Supported by Instituto Nacional de Investigacao Cientifica (Lisboa).     

Background field formalism and construction of effective action for N = 2, d = 3 supersymmetric gauge theories

We review the background field method for three-dimensional Yang-Mills and Chern-Simons models in N = 2 superspace. Superfield proper time (heat kernel) techniques are developed and exact expressions of heat kernels for constant backgrounds are presented. The background field method and heat kernel techniques are applied for evaluating the low-energy effective actions in N = 2 supersymmetric Yang-Mills and Chern-Simons models as well as in N = 4 and N = 8 SYM theories.     

Left chiral “zero modes” in a super-self-dual Yang-Mills background

A super-self-duality constraint can be imposed on the curvature two-form in supersymmetric Yang-Mills theories formulated in euclidean superspace. If left covariantly chiral superfields are coupled to such a background, part of this space of superfields is annihilated by a superspace operator constructed from the quadratic part of the action. These are analogous to the zero modes of the Dirac equation which occur in the presence of a multi-instanton. Using the supersymmetric version of the ADHM formalism, this space of left covariantly chiral “zero mode” superfields is constructed in the fundamental representation of an SU(n) gauge group. It is shown to be spanned by a set of k superfields, where k is the instanton number of the bosonic component of the Yang-Mills background.     

One-loop renormalisation of superfield Yang-Mills theories

We calculate the one-loop ultraviolet and infrared divergences in superfield Yang-Mills theories to fourth order in the gauge field. The ultraviolet divergences require a non-linear field renormalisation, and graphs with external ghost fields show that a non-linear renormalisation of the gauge-fixing function is also needed. These observations are confirmed by calculations incorporating matter fields, which are used to extend the result to all orders for the special case of SU(2). On the other hand the infrared divergences, which occur in general gauges, are apparently impossible to remove in any acceptable way.     

The vector-tensor multiplet in harmonic superspace

We describe the vector-tensor multiplet and derive its Chern-Simons coupling to the Yang-Mills gauge superfield in harmonic superspace. Received: 10 October 1997 / Published online: 23 February 1998     

On the exponentiation of leading infrared divergences in massless Yang-Mills theories

We derive, in the axial gauge, the effective U matrix which governs the behaviour of leading infrared singularities in the self-energy functions of Yang-Mills particles. We then show in a very simple manner, that these divergences, which determine the leading singularities in massless Yang-Mills theories, exponentiate.     

Global aspects of p-branes

We generalize to dimension p> 1 the notion of string structure and discuss the related obstruction. We apply our results to a model of bosonic p-branes propagating on a principal G-bundle, coupled to a Yang-Mills field and an antisymmetric tensor field and in the presence of a Wess-Zumino term in the Lagrangian. We construct the quantization line bundle and discuss the action of background gauge transformations on wave functions.     

Renormalization of Wilson operators in the light-cone gauge

We test the renormalization of Wilson operators and the Mandelstam–Leibbrandt gauge in the case when the sides of the loop are parallel to the vectors used in the M–L gauge. Graphs which in the Feynman gauge are free of ultra-violet divergences, in the M–L gauge show double divergences and single divergences with non-local Si and Ci functions. These non-local functions cancel out when we add all graphs together and the constraints of gauge invariance are satisfied. In Appendix C we briefly discuss the problems of the M–L gauge for loops containing spacelike lines. Received: 31 May 2000 / Published online: 23 January 2001     

A lagrangian formulation of the Wess approach to supersymmetric Yang-Mills theories

We obtain a superspace lagrangian density which reproduces the Wess formulation of supersymmetric gauge theories. The present approach, which is a first-order formalism, gives rise to a lagrangian density polynomial in the Yang-Mills and auxiliary superfields and appears to be stable under quantization and renormalization.     

N=1 formulation of general N=2 Yang-Mills supergravity couplings

We formulate general interactions of an N=2 Yang-Mills supermultiplet coupled to N=2 supergravity in terms of N=1 invariant functions. We show that the N=2 scalar potential of the complex scalar fields in the adjoint representation, superpartners of the Yang-Mills gauge fields, splits into a conventional gauge contribution as well as in a superpotential term contribution proportional to the SO(2) gauge coupling of N=2 de Sitter supergravity. The relation of these results to the σ model structure of N4 extended supergravities is also discussed, particularly in connection with the coset disintegration of scalar manifolds.     

Integrability on lightlike lines in six dimensional superspace

The on-shell constraint equations of extended supersymmetric Yang-Mills theories in six dimensions are shown to be integrability conditions for the superspace gauge potential on super-null-lines.     

Higher conservation laws for ten-dimensional supersymmetric Yang-Mills theories

It is shown that ten-dimensional supersymmetric Yang-Mills theories are integrable systems, in the (weak) sense of admitting a (superspace) Lax representation for their equations of motion. This is achieved by means of an explicit proof that the equations of motion are not only a consequence of but in fact fully equivalent to the superspace constraint F_αβ = 0. Moreover, a procedure for deriving infinite series of non-local conservation laws is outlined.     

Double field formulation of Yang-Mills theory

Based on our previous work on the differential geometry for the closed string double field theory, we construct a Yang-Mills action which is covariant under O(D,D) T-duality rotation and invariant under three-types of gauge transformations: non-Abelian Yang-Mills, diffeomorphism and one-form gauge symmetries. In double field formulation, in a manifestly covariant manner our action couples a single O(D,D) vector potential to the closed string double field theory. In terms of undoubled component fields, it couples a usual Yang-Mills gauge field to an additional one-form field and also to the closed string background fields which consist of a dilaton, graviton and a two-form gauge field. Our resulting action resembles a twisted Yang-Mills action.     

Cut-off versus dimensional regularization in the light-cone gauge

The conventional cut-off method is applied to massless light-cone gauge Feynman integrals. Despite the presence of non-local terms in the unintegrated expression for the Yang-Mills self-energy, the cut-off procedure yields the same ultra-violet behaviour as the lengthier technique of dimensional regularization.