Supersymmetric Formulation Research Articles

Self-dual Yang-Mills multiplet in three dimensions coupled to supergravity

We couple a recently established N=1 globally supersymmetric self-dual Yang-Mills multiplet in three dimensions to supergravity. This becomes possible due to our previous result on globally supersymmetric formulation based on a compensator multiplet. We further couple the self-dual vector to a supersymmetric {sigma}-model on the coset SO(8,n)/SO(8)xSO(n) via minimal couplings for an arbitrary gauged subgroup H{sub 0} subset of SO(8)xSO(n). A corresponding superspace formulation is also presented.

Associative-algebraic approach to logarithmic conformal field theories

We set up a strategy for studying large families of logarithmic conformal field theories by using the enlarged symmetries and non-semisimple associative algebras appearing in their lattice regularizations (as discussed in a companion paper [N. Read, H. Saleur, Enlarged symmetry algebras of spin chains, loop models, and S-matrices, cond-mat/0701259]). Here we work out in detail two examples of theories derived as the continuum limit of XXZ spin-1/2 chains, which are related to spin chains with supersymmetry algebras gl ( n | n ) and gl ( n + 1 | n ) , respectively, with open (or free) boundary conditions in all cases. These theories can also be viewed as vertex models, or as loop models. Their continuum limits are boundary conformal field theories (CFTs) with central charge c = − 2 and c = 0 respectively, and in the loop interpretation they describe dense polymers and the boundaries of critical percolation clusters, respectively. We also discuss the case of dilute (critical) polymers as another boundary CFT with c = 0 . Within the supersymmetric formulations, these boundary CFTs describe the fixed points of certain nonlinear sigma models that have a supercoset space as the target manifold, and of Landau–Ginzburg field theories. The submodule structures of indecomposable representations of the Virasoro algebra appearing in the boundary CFT, representing local fields, are derived from the lattice. A central result is the derivation of the fusion rules for these fields.

Hybrid formalism, supersymmetry reduction, and Ramond-Ramond fluxes

The supersymmetric hybrid formalism for Type II strings is used to study partial supersymmetry breaking in four and three dimensions. We use worldsheet techniques to derive effects of internal Ramond-Ramond fluxes such as torsions, superpotentials and warping.

Path integral for one-dimensional Dirac oscillator

In this paper we derive the propagator for the one-dimensional Dirac oscillator using the supersymmetric path integral formalism. The spin calculations are carried out with the help of the technique of Grassmann functional integration. The Green function is exactly evaluated. The Polyakov spin factor is explicitly derived and the energy spectrum and the corresponding wave functions are deduced.

Generalized Kähler Manifolds and Off-shell Supersymmetry

We solve the long standing problem of finding an off-shell supersymmetric formulation for a general N = (2, 2) nonlinear two dimensional sigma model. Geometrically the problem is equivalent to proving the existence of special coordinates; these correspond to particular superfields that allow for a superspace description. We construct and explain the geometric significance of the generalized Kahler potential for any generalized Kahler manifold; this potential is the superspace Lagrangian.

Self-dual non-Abelian vector multiplet in three dimensions

We present an $N=1$ supersymmetric non-Abelian compensator formulation for a vector multiplet in three dimensions. Our total field content is the off-shell vector multiplet $(A_{\ensuremath{\mu}}{}^{I},{\ensuremath{\lambda}}^{I})$ with the off-shell scalar multiplet $({\ensuremath{\varphi}}^{I},{\ensuremath{\chi}}^{I};{F}^{I})$ both in the adjoint representation of an arbitrary non-Abelian gauge group. This system is reduced to a supersymmetric $\ensuremath{\sigma}$ model on a group manifold, in the zero-coupling limit. Based on this result, we formulate a `self-dual' non-Abelian vector multiplet in three dimensions. By an appropriate identification of parameters, the mass of the self-dual vector multiplet is quantized. Additionally, we also show that the self-dual non-Abelian vector multiplet can be coupled to the supersymmetric Dirac-Born-Infeld action. These results are further reformulated in superspace to get a clear overall picture.

Arbitrary unitarily invariant random matrix ensembles and supersymmetry

We generalize the supersymmetry method in Random Matrix Theory to arbitrary rotation invariant ensembles. Our exact approach further extends a previous contribution in which we constructed a supersymmetric representation for the class of norm-dependent Random Matrix Ensembles. Here, we derive a supersymmetric formulation under very general circumstances. A projector is identified that provides the mapping of the probability density from ordinary to superspace. Furthermore, it is demonstrated that setting up the theory in Fourier superspace has considerable advantages. General and exact expressions for the correlation functions are given. We also show how the use of hyperbolic symmetry can be circumvented in the present context in which the non-linear sigma model is not used. We construct exact supersymmetric integral representations of the correlation functions for arbitrary positions of the imaginary increments in the Green functions.

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.

Superfield description of a self-dual supergravity in the context of MacDowell–Mansouri theory

Using MacDowell–Mansouri theory, in this work we investigate a superfield description of the self-dual supergravity in the context of Ashtekar theory. We find that in order to reproduce previous results on supersymmetric Ashtekar formalism, it is necessary to properly combine the supersymmetric field strength in the Lagrangian. We extend our procedure to the case of supersymmetric Ashtekar formalism in eight dimensions.

Three-flavor partially quenched chiral perturbation theory at NNLO for meson masses and decay constants

We discuss Partially Quenched Chiral Perturbation Theory (PQ$\chi$PT) and possible fitting strategies to Lattice QCD data at next-to-next-to-leading order (NNLO) in the mesonic sector. We also present a complete calculation of the masses of the charged pseudoscalar mesons, in the supersymmetric formulation of PQ$\chi$PT. Explicit analytical results are given for up to three nondegenerate sea quark flavors, along with the previously unpublished expression for the pseudoscalar meson decay constant for three nondegenerate sea quark flavors. The numerical analysis in this paper demonstrates that the corrections at NNLO are sizable, as expected from earlier work.

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.

Partial supersymmetry breaking and [formula omitted][formula omitted] gauge model with hypermultiplets in harmonic superspace

We provide a manifestly N = 2 supersymmetric formulation of the N = 2 U ( N c ) gauge model constructed in terms of N = 1 superfields in hep-th/0409060. The model is composed of N = 2 vector multiplets in harmonic superspace and can be viewed as the N = 2 U ( N c ) Yang–Mills effective action equipped with the electric and magnetic Fayet–Iliopoulos terms. We generalize this gauge model to an N = 2 U ( N c ) QCD model by introducing N = 2 hypermultiplets in harmonic superspace which include both the fundamental representation of U ( N c ) and the adjoint representation of U ( N c ) . The effect of the magnetic Fayet–Iliopoulos term is to shift the auxiliary field by an imaginary constant. Examining vacua of the model, we show that N = 2 supersymmetry is spontaneously broken down to N = 1 .

Quantum Hall liquid on a noncommutative superplane

Supersymmetric quantum Hall liquids are constructed on a noncommutative superplane. We explore a supersymmetric formalism of the Landau problem. In the lowest Landau level, there appear spin-less bosonic states and spin-1/2 down fermionic states, which exhibit a super-chiral property. It is shown the Laughlin wavefunction and topological excitations have their superpartners. Similarities between supersymmetric quantum Hall systems and bilayer quantum Hall systems are discussed.

Masses and decay constants of pseudoscalar mesons to two loops in two-flavor partially quenched chiral perturbation theory

This paper presents a first study of the masses and decay constants of the charged, or flavor-off-diagonal, pseudoscalar mesons to two loops for two flavors of sea-quarks, in Partially Quenched Chiral Perturbation Theory (PQ$\chi$PT). Explicit analytical expressions up to ${\cal O}(p^6)$ in the momentum expansion are given. The calculations have been performed within the supersymmetric formulation of PQ$\chi$PT. A numerical analysis is done to indicate the size of the corrections.

Decay constants of pseudoscalar mesons to two loops in three-flavor partially quenched chiral perturbation theory

This paper presents a first study of the decay constants of the charged, or flavor-off-diagonal, pseudoscalar mesons to two loops for three flavors of sea quarks, in Partially Quenched Chiral Perturbation Theory (PQ$\chi$PT). Explicit analytical expressions up to ${\cal O}(p^6)$ in the momentum expansion are given. The calculations have been performed within the supersymmetric formulation of PQ$\chi$PT. We also present some numerical results to indicate the size of the corrections.

Eleven dimensional supergravity in light cone gauge

Light-cone gauge manifestly supersymmetric formulation of eleven dimensional supergravity is developed. The formulation is given entirely in terms of light cone scalar superfield, allowing us to treat all component fields on an equal footing. All higher derivative on mass shell manifestly supersymmetric 4-point functions invariant with respect to linear supersymmetry transformations and corresponding (in gravitational bosonic sector) to terms constructed from four Riemann tensors and derivatives are found. Superspace representation for 4-point scattering amplitudes is also obtained. Superfield representation of linearized interaction vertex of superparticle and supergravity fields is presented. All 4-point higher derivative interaction vertices of ten-dimensional supersymmetric Yang-Mills theory are also determined.

TAP complexity, the cavity method and supersymmetry

We compute the Bray and Moore (BM) TAP Complexity for the Sherrington-Kirkpatrick model through the cavity method, showing that some essential modifications are needed with respect to the standard formulation of the method. This allows to understand various features recently discovered and to unveil at last the physical meaning of the parameters of the BM theory. We also reconsider the supersymmetric (SUSY) formulation of the problem finding that the BM solution satisfies some proper SUSY Ward identities that are different from the standard ones. The SUSY relationships encode the physical meaning of the parameters obtained through the cavity method. The problem of the vanishing prefactor is addressed showing how it can be avoided.

Network Models in Class C on Arbitrary Graphs

We consider network models of quantum localisation in which a particle with a two-component wave function propagates through the nodes and along the edges of an arbitrary directed graph, subject to a random SU(2) rotation on each edge it traverses. The propagation through each node is specified by an arbitrary but fixed S-matrix. Such networks model localisation problems in class C of the classification of Altland and Zirnbauer [1], and, on suitable graphs, they model the spin quantum Hall transition. We extend the analyses of Gruzberg, Ludwig and Read [5] and of Beamond, Cardy and Chalker [2] to show that, on an arbitrary graph, the mean density of states and the mean conductance may be calculated in terms of observables of a classical history-dependent random walk on the same graph. The transition weights for this process are explicitly related to the elements of the S-matrices. They are correctly normalised but, on graphs with nodes of degree greater than 4, not necessarily non-negative (and therefore interpretable as probabilities) unless a sufficient number of them happen to vanish. Our methods use a supersymmetric path integral formulation of the problem which is completely finite and rigorous.

An SL(2,ℝ)‐covariant, first order, κ‐supersymmetric action for the D5‐brane

AbstractThe new first order, rheonomic, κ–supersymmetric formalism recently introduced by us for the world‐volume action of the D3 brane is extended to the case of D5 branes. This extension requires the dual formulation of the Free Differential Algebra of type IIB supergravity in terms of 6–form gauge potentials which was so far missing and is given here. Furthermore relying on our new approach we are able to write the D5 world volume action in a manifestly SL(2,ℝ) covariant form. This is important in order to solve the outstanding problem of finding the appropriate boundary actions of D3–branes on smooth ALE manifolds with twisted fields. The application of our results to this problem is however postponed to a subsequent publication.

Non-BPS D-branes in light-cone Green-Schwarz formalism

Non-BPS D-branes are difficult to describe covariantly in a manifestly supersymmetric formalism. For definiteness we concentrate on type IIB string theory in flat background in light-cone Green-Schwarz formalism. We study both the boundary state and the boundary conformal field theory descriptions of these D-branes with manifest SO(8) covariance and go through various consistency checks. We analyze Sen's original construction of non-BPS D-branes given in terms of an orbifold boundary conformal field theory. We also directly study the relevant world-sheet theory by deriving the open string boundary condition from the covariant boundary state. Both these methods give the same open string spectrum which is consistent with the boundary state, as required by the world-sheet duality. The boundary condition found in the second method is given in terms of bi-local fields that are quadratic in Green-Schwarz fermions. We design a special ``doubling trick'' suitable to handle such boundary conditions and prescribe rules for computing all possible correlation functions without boundary insertions. This prescription has been tested by computing disk one-point functions of several classes of closed string states and comparing the results with the boundary state computation.