Supersymmetric Sigma Research Articles

Renormalons in integrable field theories

In integrable field theories in two dimensions, the Bethe ansatz can be used to compute exactly the ground state energy in the presence of an external field coupled to a conserved charge. We generalize previous results by Volin and we extract analytic results for the perturbative expansion of this observable, up to very high order, in various asymptotically free theories: the non-linear sigma model and its supersymmetric extension, the Gross-Neveu model, and the principal chiral field. We study the large order behavior of these perturbative series and we give strong evidence that, as expected, it is controlled by renormalons. Our analysis is sensitive to the next-to-leading correction to the asymptotics, which involves the first two coefficients of the beta function. We also show that, in the supersymmetric non-linear sigma model, there is no contribution from the first IR renormalon, in agreement with general arguments.

Interaction of supersymmetric nonlinear sigma models with external higher spin superfields via higher spin supercurrents

We consider a four dimensional generalized Wess-Zumino model formulated in terms of an arbitrary Kähler potential mathcal{K}left(varPhi, overline{varPhi}right) and an arbitrary chiral superpotential mathcal{W}left(varPhi right) . A general analysis is given to describe the possible interactions of this theory with external higher spin gauge superfields of the (s + 1, s + 1/2) supermultiplet via higher spin supercurrents. It is shown that such interactions do not exist beyond supergravity (s ≥ 2) for any mathcal{K} and mathcal{W} . However, we find three exceptions, the theory of a free massless chiral, the theory of a free massive chiral and the theory of a free chiral with linear superpotential. For the first two, the higher spin supercurrents are known and for the third one we provide the explicit expressions. We also discuss the lower spin supercurrents. As expected, a coupling to (non-minimal) supergravity (s = 1) can always be found and we give the generating supercurrent and supertrace for arbitrary mathcal{K} and mathcal{W} . On the other hand, coupling to the vector supermultiplet (s = 0) is possible only if mathcal{K} = mathcal{K}left(overline{varPhi}varPhi right) and mathcal{W}=0 .

Regularity of Solutions of the Nonlinear Sigma Model with Gravitino

We propose a geometric setup to study analytic aspects of a variant of the super symmetric two-dimensional nonlinear sigma model. This functional extends the functional of Dirac-harmonic maps by gravitino fields. The system of Euler–Lagrange equations of the two-dimensional nonlinear sigma model with gravitino is calculated explicitly. The gravitino terms pose additional analytic difficulties to show smoothness of its weak solutions which are overcome using Rivière’s regularity theory and Riesz potential theory.

A comparison of a nonlinear sigma model with general pinning and pinning at one point

We study the nonlinear supersymmetric hyperbolic sigma model introduced by Zirnbauer in 1991. This model can be related to the mixing measure of a vertex-reinforced jump process. We prove that the two-point correlation function has a probabilistic interpretation in terms of connectivity in rooted random spanning forests. Using this interpretation, we dominate the two-point correlation function for general pinning, e.g. for uniform pinning, with the corresponding correlation function with pinning at one point. The result holds for a general finite graph, asymptotically as the strength of the pinning converges to zero. Specializing this to general ladder graphs, we deduce in the same asymptotic regime exponential decay of correlations for general pinning.

Family unification via quasi-Nambu–Goldstone fermions in string theory

Some of the supersymmetric nonlinear sigma models on exceptional groups (E7 or E8) are known to yield almost minimal necessary content of matter fields for phenomenological model building, including three chiral families and a Higgs multiplet. We explore a possible realization of such a family unification in heterotic string theory, where the spontaneously broken symmetry that we focus on is the one associated with the change of global orientation of the spin bundle embedded in the gauge bundle, which cannot be ignored in the presence of a magnetic source of the B field. We show in a simple model that it indeed gives rise to chiral matter fields on the defect similarly to the domain-wall fermions, and compare the chiral zero mode spectrum with the sigma model. The setup is reduced to a system similar to that postulated in the orbifold GUT or the grand gauge-Higgs unification model, where the origin of Z2 identification is accounted for as arising from the bolt of the Atiyah-Hitchin manifold.

REAL AND COMPLEX SUPERSYMMETRIC d = 1 SIGMA MODELS WITH TORSIONS

We derive and discuss, at both the classical and quantum levels, generalized [Formula: see text] supersymmetric quantum mechanical sigma models describing the motion over an arbitrary real or an arbitrary complex manifold with extra torsions. We analyze the relevant vacuum states to make explicit the fact that their number is not affected by adding the torsion terms.

BRST treatment of zero modes for the worldline formalism in curved space

One-loop quantities in QFT can be computed in an efficient way using the worldline formalism. The latter rests on the ability of calculating 1D path integrals on the circle. In this paper we give a systematic discussion for treating zero modes on the circle of 1D path integrals for both bosonic and supersymmetric nonlinear sigma models, following an approach originally introduced by Friedan. We use BRST techniques and place a special emphasis on the issue of reparametrization invariance. Various examples are extensively analyzed to verify and test the general set-up. In particular, we explicitly check that the chiral anomaly, which can be obtained by the semiclassical approximation of a supersymmetric 1D path integral, does not receive higher order worldline contributions, as implied by supersymmetry.

Lorentz invariance and supersymmetry of four particle scattering amplitudes in theSNR8orbifold sigma model

The $S^N\R^8$ supersymmetric orbifold sigma model is expected to describe the IR limit of the Matrix string theory. In the framework of the model the type IIA string interaction is governed by a vertex which was recently proposed by R.Dijkgraaf, E.Verlinde and H.Verlinde. By using this interaction vertex we derive all four particle scattering amplitudes directly from the orbifold model in the large $N$ limit.

Algebra of Nonlocal Charges in Supersymmetric Nonlinear Sigma Models

We propose a graphic method to derive the classical algebra (Dirac brackets) of nonlocal conserved charges in the two-dimensional supersymmetric nonlinear O(N) sigma model. As in the purely bosonic theory we find a cubic Yangian algebra. We also consider the extension of graphic methods to other integrable theories.

SYMPLECTIC QUANTIZATION OF SUPERFIELDS

We show how the extension of the Faddeev-Jackiw symplectic quantization (including true constraints) can be used in superspace. We first deal with supersymmetric free field theory in the component language. After that, we consider the method applied to superfields, taken as canonical variables. We also use the formalism, directly in superfield formulation, for the supersymmetric nonlinear sigma model.

New geometry from heterotic supersymmetry

The authors show that the bosonic sector of a (4,0) supersymmetric sigma -model is a quasi Ricci-flat manifold with a closed torsion and vanishing scalar curvature; in the torsionless limit they recover the hyper-Kahler (4,4) models. Using the harmonic superspace and the self-duality equations they derive the (4,0) generalizations of the metrics of Taub-NUT and Eguchi-Hanson.

Explicit Construction of Supercharges of Supersymmetric Nonlinear Sigma Models in 1 + 1 Spacetime Dimensions

Considering the N = 1 supersymmetry transformations of supersymmetric nonlinear sigma models in 1 + 1 dimensions we construct explicitly conserved Noether currents associated with supersymmetry transformations and derive the associated conserved charges in terms of the basic fields. We compare this result with superspace calculations. Finally we review the connection between extended supersymmetry and the geometry of the target space and derive an explicit form of the supercharges for extended supersymmetry.

Explicit Construction of Supercharges of Supersymmetric Nonlinear Sigma Models in 1 + 1 Spacetime Dimensions

Explicit Construction of Supercharges of Supersymmetric Nonlinear Sigma Models in 1 + 1 Spacetime Dimensions

Geometry of sigma -models with heterotic supersymmetry

The authors apply the method of harmonic superspace for solving locally the torsion constraints for the manifolds of (4, 0) supersymmetric sigma -models. The solution is given in terms of an unconstrained harmonic-analytic prepotential with a curved vector index. This prepotential also determines the form of the most general off-shell (4, 0) sigma -model action. The torsion-free (hyper-Kahler) case is recovered if one takes the gradient of a scalar analytic superfield as the vector potential.

SUPERSYMMETRIC TENSOR GAUGE THEORIES

The supersymmetric extensions of anti-symmetric tensor gauge theories and their associated tensor gauge symmetry transformations are constructed. The classical equivalence between such supersymmetric tensor gauge theories and supersymmetric non-linear sigma models is established. The global symmetry of the supersymmetric tensor gauge theory is gauged and the locally invariant action is obtained. The supercurrent on the Kähler manifold is found in terms of the supersymmetric tensor gauge field.

TheE 8/E 7×U(1) supersymmetric sigma model

The Kahler potential of the homogeneous Kahler manifoldE8/E7×U(1), and hence the Lagrangian of the corresponding supersymmetric nonlinear sigma model, is constructed in explicit form.

O(2) string theory with a Wess-Zumino term.

N-italic = 2 chiral conformal supergravity is coupled to a (2,0) supersymmetric nonlinear sigma model with a Wess-Zumino term. This Lagrangian can describe a consistent O(2) string theory in more than 2 space-time dimensions.

Group structure of hidden symmetry transformations for supersymmetric nonlinear sigma models

The author investigates the group structure of the hidden symmetry transformations for classical two-dimensional supersymmetric generalized nonlinear sigma models. It is shown that the generators with positive and with negative index separately form infinite closed Lie algebras isomorphic to the algebra that is partially the Lie algebra of the subgroup G that leaves the initial data invariant and F(t) is the class of rational functions.

Supersymmetric nonlinear sigma models constrained on non-compact manifold

A detailed analysis by 1/n expansion is presented of supersymmetric nonlinear sigma models in two dimensions withU(n) symmetry in which the scalar fields are constrained on a non-compact manifold. The theories are ultraviolet finite. In the massless version of the models no mass scale is generated and gauge bosons fail to get dynamics while this is possible provided the theory contains a mass scale. The effects of introduction of the “O-term” into supersymmetric theories are also discussed. In particular, it is argued that supersymmetry is broken by the O-term only in finite supersymmetric theories. Finally, a singular behavior in the massless limit in these models is pointed out.

Classical Solutions for the Supersymmetric Grassmannian Sigma Models in Two Dimensions. II

On etudie la version supersymetrique des modeles sigma complexes grassmanniens a 2 dimensions euclidiennes. On construit des solutions fermion classiques explicites pour les equations de Dirac supersymetriques linearisees