Supergraph Techniques Research Articles

Quadratic contributions of softly broken supersymmetry in the light of loop regularization

Loop regularization (LORE) is a novel regularization scheme in modern quantum field theories. It makes no change to the spacetime structure and respects both gauge symmetries and supersymmetry. As a result, LORE should be useful in calculating loop corrections in supersymmetry phenomenology. To further demonstrate its power, in this article we revisit in the light of LORE the old issue of the absence of quadratic contributions (quadratic divergences) in softly broken supersymmetric field theories. It is shown explicitly by Feynman diagrammatic calculations that up to two loops the Wess–Zumino model with soft supersymmetry breaking terms (WZ’ model), one of the simplest models with the explicit supersymmetry breaking, is free of quadratic contributions. All the quadratic contributions cancel with each other perfectly, which is consistent with results dictated by the supergraph techniques.

Twisted superspace: Non-renormalization and fermionic symmetries in certain heterotic-string-inspired non-supersymmetric field theories

Inspired by the tachyon-free non-supersymmetric heterotic SO(16)xSO(16) string we consider a special class of non-supersymmetric field theories: Those that can be obtained from supersymmetric field theories by supersymmetry breaking twists. We argue that such theories, like their supersymmetric counter parts, may still possess some fermionic symmetries as left-overs of the super gauge transformations and have special one-loop non-renormalization properties due to holomorphicity. In addition, we extend the supergraph techniques to these theories to calculate some explicit supersymmetry-breaking corrections.

One-loop right-handed neutrino threshold corrections for two-loop running in supersymmetric type I seesaw models

The renormalization group (RG) running of the neutrino mass operator is required for comparing the predictions of neutrino models at high energy with the experimental data at low energies. In the type I seesaw scenario with n_G right-handed neutrinos, the RG running is also performed in the effective theories above and between the thresholds given by the masses of the right-handed neutrinos. At these thresholds, the effective theories are matched. When calculating the two-loop RG running, the matching has to be performed at the one-loop level. In this work, we calculate the one-loop matching formulae in the MSSM extended by n_G right-handed neutrinos using supergraph techniques. Moreover we present a general formula for one-loop matching of superpotential operators which can readily be applied to any supersymmetric theory where chiral superfields are integrated out.

Supergraph approach in a higher-order linear delta expansion calculation of the effective potential forF-type broken supersymmetry

In this work, we adopt the simplest model that spontaneously breaks supersymmetry, namely, the minimal O'Raifeartaigh model. The effective potential is computed in the framework of the linear delta expansion approach up to the order ${\ensuremath{\delta}}^{2}$, conjugated with superspace and supergraph techniques. The latter can be duly mastered even if supersymmetry is no longer exact, and the efficacy of the superfield approach in connection with the linear delta expansion procedure is confirmed according to our investigation. That opens up a way for a semi-nonperturbative superspace computation that allows us to deal with spontaneously broken supersymmetric models and encourages us to go further and apply this treatment to the minimal supersymmetric Standard Model precision tests.

Supergraph techniques forD=3,N=1broken supersymmetric theories

We enlarge the usual D=3 N=1 supergraph techniques to include the case of (explicitly or spontaneously) broken supersymmetric gauge theories. To illustrate the utility of these techniques, we calculate the two-loop effective potential of the SQED3 by using the tadpole and the vacuum bubble methods. In these methods, to investigate the possibility of supersymmetry breaking, the superfields must be shifted by $\theta$ dependent classical superfields (vacuum expectation values), what implies in the explicit breakdown of supersymmetry in the intermediate steps of the calculation. Nevertheless, after studying the minimum of the resulting effective potential, we find that supersymmetry is conserved, while gauge symmetry is dynamically broken, with a mass generated for the gauge superfield.

Marginal deformations and 3-algebra structures

We study marginal deformations of superconformal Chern–Simons matter theories that are based on 3-algebras. For this, we introduce the notion of an associated 3-product, which captures very general gauge invariant deformations of the superpotentials of the BLG and ABJM models. We also consider conformal multi-trace deformations preserving N = 2 supersymmetry. We then use N = 2 supergraph techniques to compute the two-loop beta functions of these deformations. Besides confirming conformal invariance of both the BLG and ABJM models, we also verify that the recently proposed β-deformations of the ABJM model are indeed marginal to the order we are considering.

Five-dimensional supersymmetric Chern–Simons action as a hypermultiplet quantum correction

Abstract Building on the covariant supergraph techniques in 4D N = 2 harmonic superspace, we develop a manifestly 5D N = 1 supersymmetric and gauge covariant formalism to compute the one-loop effective action for a hypermultiplet coupled to a background vector multiplet. As a simple application, we demonstrate the generation of a supersymmetric Chern–Simons action at the quantum level, both in the Coulomb and the non-Abelian phases. These superfield results are in agreement with the earlier component considerations of Seiberg et al. Our analysis suggests that similar calculations in terms of hybrid 4D superfields or within the 5D projective superspace approach may allow one to extract suitable formulations for the non-Abelian 5D supersymmetric Chern–Simons theory.

Quantum corrections to non-Abelian SUSY theories on orbifolds

We consider supersymmetric non-Abelian gauge theories coupled to hyper multiplets on five and six dimensional orbifolds, S 1 / Z 2 and T 2 / Z N , respectively. We compute the bulk and local fixed point renormalizations of the gauge couplings. To this end we extend supergraph techniques to these orbifolds by defining orbifold compatible delta functions. We develop their properties in detail. To cancel the bulk one-loop divergences the bulk gauge kinetic terms and dimension six higher derivative operators are required. The gauge couplings renormalize at the Z N fixed points due to vector multiplet self interactions; the hyper multiplet renormalizes only non- Z 2 fixed points. In 6D the Wess–Zumino–Witten term and a higher derivative analogue have to renormalize in the bulk as well to preserve 6D gauge invariance.

On supersymmetry breaking and the Dijkgraaf-Vafa conjecture

We investigate the Dijkgraaf-Vafa proposal when supersymmetry is broken. We consider U(N) SYM with chiral adjoint matter where the coupling constants in the tree-level superpotential are promoted to chiral spurions. The holomorphic part of the low-energy glueball superpotential can still be analyzed. We compute the holomorphic supersymmetry breaking contributions using methods of the geometry underlying the N=1 effective gauge theory viewed as a Whitham system. We also study the change in the effective glueball superpotential using perturbative supergraph techniques in the presence of spurions.

On five-dimensional superspaces

Recent one-loop calculations of certain supergravity-mediated quantum corrections in supersymmetric brane-world models employ either the component formulation (hep-th/0305184) or the superfield formalism with only half of the bulk supersymmetry manifestly realized (hep-th/0305169 and hep-th/0411216). There are reasons to expect, however, that 5D supergraphs provide a more efficient setup to deal with these and more involved (in particular, higher-loop) calculations. As a first step toward elaborating such supergraph techniques, we develop in this letter a manifestly supersymmetric formulation for 5D globally supersymmetric theories with eight supercharges. Simple rules are given to reduce 5D superspace actions to a hybrid form which keeps manifest only the 4D, N=1 Poincare supersymmetry. (Previously, such hybrid actions were carefully worked out by rewriting the component actions in terms of simple superfields). To demonstrate the power of this formalism for model building applications, two families of off-shell supersymmetric nonlinear sigma-models in five dimensions are presented (including those with cotangent bundles of Kahler manifolds as target spaces). We elaborate, trying to make our presentation maximally clear and self-contained, on the techniques of 5D harmonic and projective superspaces used at some stages in this letter.

Renormalization of supersymmetric gauge theories on orbifolds: Brane gauge couplings and higher derivative operators

We consider supersymmetric gauge theories coupled to hypermultiplets on five- and six-dimensional orbifolds and determine the bulk and local fixed point renormalizations of the gauge couplings. We infer from a component analysis that the hypermultiplet does not induce renormalization of the brane gauge couplings on the five-dimensional orbifold S1/Z2. This is not due to supersymmetry, since the bosonic and fermionic contributions cancel separately. We extend this investigation to T2/ZN orbifolds using supergraph techniques in six dimensions. On general ZN orbifolds the gauge couplings do renormalize at the fixed points, except for the Z2 fixed points of even ordered orbifolds. To cancel the bulk one-loop divergences a dimension six higher derivative operator is needed, in addition to the standard bulk gauge kinetic term.

Covariant quantization of N=1/2 SYM theories and supergauge invariance

So far, quantum properties of N=1/2 nonanticommutative (NAC) super Yang--Mills theories have been investigated in the WZ gauge. The gauge independence of the results requires assuming that at the quantum level supergauge invariance is not broken by nonanticommutative geometry. In this paper we use an alternative approach which allows studying these theories in a manifestly gauge independent superspace setup. This is accomplished by generalizing the background field method to the NAC case, by moving to a momentum superspace where star products are treated as exponential factors and by developing momentum supergraph techniques. We compute the one--loop gauge effective action for NAC U(N) gauge theories with matter in the adjoint representation. Despite the appearance of divergent contributions which break (super)gauge invariance, we prove that the effective action at this order is indeed invariant.

Two-loop renormalization for nonanticommutativeN= 1/2 supersymmetric WZ model

We study systematically, through two loops, the divergence structure of the supersymmetric WZ model defined on the N=1/2 nonanticommutative superspace. By introducing a spurion field to represent the supersymmetry breaking term F^3 we are able to perform our calculations using conventional supergraph techniques. Divergent terms proportional to F, F^2 and F^3 are produced (the first two are to be expected on general grounds) but no higher-point divergences are found. By adding ab initio F and F^2 terms to the original lagrangian we render the model renormalizable. We determine the renormalization constants and beta functions through two loops, thus making it possible to study the renormalization group flow of the nonanticommutation parameter.

Complete low-energy effective action in [formula omitted] SYM: a direct [formula omitted] supergraph calculation

Using the covariant N=2 harmonic supergraph techniques we calculate the one-loop low-energy effective action of N=4 super-Yang–Mills theory in Coulomb branch with gauge group SU(2) spontaneously broken down to U(1). The full dependence of the low-energy effective action on both the hypermultiplet and gauge fields is determined. The direct quantum calculation confirms the correctness of the exact N=4 SYM low-energy effective action derived in hep-th/0111062 on the purely algebraic ground by invoking a hidden N=2 supersymmetry which completes the manifest N=2 one to N=4 . Our results provide an exhaustive solution to the problem of finding out the exact completely N=4 supersymmetric low-energy effective action for the theory under consideration.

Supergraph Techniques and Two-Loop Beta-Functions for Renormalizable and Non-Renormalizable Operators

We present a construction kit for calculating two-loop beta functions in N=1 supersymmetric theories for the operators of the superpotential using supergraph techniques. In particular, it allows to compute the beta functions for every desired, even higher dimensional, operator of the superpotential from the wavefunction renormalization constants of the theory. We apply this method to calculate the two-loop beta functions for the lowest-dimensional effective neutrino mass operator in the Minimal Supersymmetric Standard Model (MSSM) and for the Yukawa couplings in the MSSM extended by singlet superfields and the mass matrix for the latter. Our method can be applied to any N=1 supersymmetric theory.

Effective action of the N = 2 Maxwell multiplet in harmonic superspace

We present, in the N=2, D=4 harmonic superspace formalism, a general method for constructing the off-shell effective action of an N=2 abelian gauge superfield coupled to matter hypermultiplets. Using manifestly N=2 supersymmetric harmonic supergraph techniques, we calculate the low-energy corrections to the renormalized one-loop effective action in terms of N=2 (anti)chiral superfield strengths. For a harmonic gauge prepotential with vanishing vacuum expectation value, corresponding to massless hypermultiplets, the only non-trivial radiative corrections to appear are non-holomorphic. For a prepotential with non-zero vacuum value, which breaks the U(1)-factor in the N=2 supersymmetry automorphism group and corresponds to massive hypermultiplets, only non-trivial holomorphic corrections arise at leading order. These holomorphic contribution are consistent with Seiberg's quantum correction to the effective action, while the first non-holomorphic contribution in the massless case is the N=2 supersymmetrization of the Heisenberg-Euler effective Lagrangian.

Topology and heterotic, gravitational, Lorentz and super-Weyl anomalies

The (1,0) superdiffeomorphic and Lorentz anomalies are constructed using cohomology and descent equations in heterotic superspace. The superfield gravitational Wess-Zumino term is presented. Supergraph techniques are used to calculate the coefficients of the superdiffeomorphic, Lorentz and super-Weyl anomalies.

Broken (1, 0) supergraphity

The usual (1, 0) supergraph techniques are extended to account for supersymmetry breaking terms. Several possible breaking lagrangians are contemplated and the consistency of our modified super-Feynman rules is checked through a number of explicit supergraph evaluations. They might be of practical relevance in dealing with non-linear σ-models whenever supersymmetry is broken.

Cohomology and heterotic world-sheet anomalies.

Topological methods are applied to calculating world-sheet anomalies in (p,q) supersymmetry. Specifically, we construct the (1,0) gauge anomaly using cohomology and the descent equations in (1,0) superspace. The coefficient of the anomaly is calculated with supergraph techniques.

A simple implementation of Wess-Zumino-like gauges within the superfield technique

Within the context of the superfield formalism we present a class of Wess-Zumino-like gauges induced by a simple non-supersymmetric gauge fixing term, thus eliminating the spurious infrared singularity of the vector-superfield propagator without abandoning the efficiency of supergraph techniques.