Dynamical supersymmetry breaking is an important issue for applications of supersymmetry in particle physics. The functional renormalization group equations allow for a nonperturbative approach that leaves supersymmetry intact. Therefore they offer a promising tool to investigate dynamical supersymmetry breaking. Here we will employ this method to derive the phase diagram and a surprisingly rich RG fixed-point structure with corresponding critical exponents for the $\mathcal N=1$ Wess-Zumino model in two dimensions.
We present BPS solutions to a general class of Wess-Zumino models which extend previous results in the literature. We discuss their relation to amplitudes on threshold, and their application to scalar domain walls in Supersymmetric QCD. We also find partial expressions for Wess-Zumino models with softly broken supersymmetry.
Using a non-perturbative functional method, where the quantum fluctuations are gradually set up,it is shown that the interaction of a N=1 Wess-Zumino model in 2+1 dimensions does not get renormalized. This result is valid in the framework of the gradient expansion and aims at compensating the lack of non-renormalization theorems.
Using the nonrenormalization theorem and Pohlmeyer's theorem, it is proven that there cannot be an asymptotic safety scenario for the Wess-Zumino model unless there exists a non-trivial fixed point with (i) a negative anomalous dimension (ii) a relevant direction belonging to the Kaehler potential.
Sigma models in which the integer coefficient of the Wess-Zumino term vanishes are easy to construct. This is the case if all flavor symmetries are vectorlike. We show that there is a subset of SU(N)XSU(N) vectorlike sigma models in which the Wess-Zumino term vanishes for reasons of symmetry as well. However, there is no chiral sigma model in which the Wess-Zumino term vanishes for reasons of symmetry. This can be understood in the sigma model basis as a consequence of an index theorem for the axialvector coupling matrix. We prove this index theorem directly from the SU(N)XSU(N) algebra.
We prove that the Wess-Zumino model breaks supersymmetry in the low-energy limit. The mechanism is identical to the breaking of chiral symmetry in quantum chromodynamics as the low-energy limit is a Nambu-Jona-Lasinio model and the gap equation has a solution. This happens at a critical coupling at lower momenta. Instanton liquid plays an essential role in the behavior of the theory in this limit.
The Nelson-Seiberg theorem and its extensions relate supersymmetry breaking and R-symmetries in Wess-Zumino models. But their applicability may be limited by previously found non-generic counterexamples. Constructing a dataset of R-symmetric Wess-Zumino models is useful for studying the occurrence of such counterexamples as well as other purposes. This work gives a pedagogical review on the basics of supersymmetry in (3+1)-dimensions, Wess-Zumino models and their supergravity extensions, the Nelson-Seiberg theorem and its extensions. We present a preliminary construction of the dataset of R-sy…
It is known in previous literature that if a Wess-Zumino model with an R-symmetry gives a supersymmetric vacuum, the superpotential vanishes at the vacuum. In this work, we establish a formal notion of genericity, and show that if the R-symmetric superpotential has generic coefficients, the superpotential vanishes term-by-term at a supersymmetric vacuum. This result constrains the form of the superpotential which leads to a supersymmetric vacuum. It may contribute to a refined classification of R-symmetric Wess-Zumino models, and find applications in string constructions of vacua with small su…
We construct the Bardeen anomaly and its related Wess-Zumino term in the supersymmetric standard model. In particular we show that it can be written in terms of a composite linear superfield related to supersymmetrized Chern-Simons forms, in very much the same way as the Green-Schwarz term in four-dimensional string theory. Some physical applications, such as the contribution to the g-2 of gauginos when a heavy top is integrated out, are briefly discussed.
We study aspects of Wess-Zumino models related to SUSY and R-symmetry breaking at tree-level. We present a recipe for constructing a wide class of tree-level SUSY and R-breaking models. We also deduce a general property shared by all tree-level SUSY breaking models that has broad application to model building. In particular, it explains why many models of direct gauge mediation have anomalously light gauginos (even if the R-symmetry is broken spontaneously by an order one amount). This suggests new approaches to dynamical SUSY breaking which can generate large enough gaugino masses.
The renormalization of N=1 Super Yang-Mills theory is analysed in the Wess-Zumino gauge, employing the Landau condition. An all orders proof of the renormalizability of the theory is given by means of the Algebraic Renormalization procedure. Only three renormalization constants are needed, which can be identified with the coupling constant, gauge field and gluino renormalization. The non-renormalization theorem of the gluon-ghost-antighost vertex in the Landau gauge is shown to remain valid in N=1 Super Yang-Mills. Moreover, due to the non-linear realization of the supersymmetry in the Wess-Zu…
We prove that the covariant and Hamiltonian phase spaces of the Wess-Zumino-Witten model on the cylinder are diffeomorphic and we derive the Poisson brackets of the theory.
We show the equivalence between Stuckelberg and Wess-Zumino methods of restoration of gauge symmetries of the anomalous, Abelian, effective action, in arbitrary even dimensions D=2k. We present dual version of Wess-Zumino terms with the compensating field described by a Kalb-Ramond like p=2k-2 form.
Lie algebra valued equations translating the integrability of a general two-dimensional Wess-Zumino-Witten model are given. We found simple solutions to these equations and identified three types of new integrable non-linear sigma models. One of them is a modified Yang-Baxter sigma model supplemented with a Wess-Zumino-Witten term.
The phase space of the Wess-Zumino-Witten model on a circle with target space a compact, connected, semisimple Lie group $G$ is defined and the corresponding symplectic form is given. We present a careful derivation of the Poisson brackets of the Wess-Zumino-Witten model. We also study the canonical structure of the supersymmetric and the gauged Wess-Zumino-Witten models.
We investigate the non-abelian $T$-duality of Wess-Zumino-Witten model. The obtained dual model is equivalent to the model dual to the $SU(2)$ chiral model found by Curtright-Zachos. This might tell that the Wess-Zumino term would be induced when the chiral model couples with gravity.
We illustrate the causal perturbation and causal renormalization method (the Epstein-Glaser method) for the case of the supersymmetric Wess-Zumino model. Our study is based on the Hilbert space structure of the N=1 superspace.
In a recent paper, based on the Skyrme model with the Wess-Zumino-Witten term including electromagnetism, Eto et al. pointed out an intriguing possibility that the Gell-Mann-Nishijima relation is corrected under the presence of back-ground electromagnetic fields, thereby being led to the conclusion that even a neutron acquires non-zero net charge in external magnetic fields. We point out that this remarkable conclusion is inseparably connected with an unwelcome feature of the gauged Wess-Zumino-Witten action, i.e. the non-conservation of source current of Maxwell equation.
The Wess-Zumino couplings for generalized sigma-orbifold fixed-points are presented and the generalized GS 6-form that encoding the complete sigma-standard gauge-gravitational-non standard gauge anomaly and its opposite inflow is derived.
It is argued that, in the two dimensional principal chiral model, the Wess-Zumino term can be induced quantum mechanically, allowing the model with the critical value of the coupling constant $λ^2 = 8π/|k|$ to turn into the Wess-Zumino-Novikov-Witten model at the quantum level. The Wess-Zumino term emerges from the inequivalent quantizations possible on a sphere hidden in the configuration space of the original model. It is shown that the Dirac monopole potential, which is induced on the sphere in the inequivalent quantizations, turns out to be the Wess-Zumino term in the entire configuration …
We analyze the noncommutative two-dimensional Wess-Zumino-Witten model and its properties under Seiberg-Witten transformations in the operator formulation. We prove that the model is invariant under such transformations even for the noncritical (non chiral) case, in which the coefficients of the kinetic and Wess-Zumino terms are not related. The pure Wess-Zumino term represents a singular case in which this transformation fails to reach a commutative limit. We also discuss potential implications of this result for bosonization.
We examine a bilinear form Wess-Zumino term for a superstring in anti-de Sitter (AdS) spaces. This is composed of two parts; a bilinear term in superinvariant currents and a total derivative bilinear term which is required for the pseudo-superinvariance of the Wess-Zumino term. The covariant supercharge commutator containing a string charge is also obtained.
We present a general formula for the Wess-Zumino action associated with the Weyl anomaly, given in a curved background for any even number of dimensions. The result is obtained by considering a finite Weyl transformation of counterterms in dimensional regularization.
We study the renormalization group flow properties of the Wess-Zumino-Witten model in the region of couplings between $g^2=0$ and $g^2=4π/k$, by evaluating the two-loop Zamolodchikov's $c$-function. We also discuss the region of negative couplings.
We deform the well-known three dimensional $\mathcal{N}=1$ Wess-Zumino model by adding higher derivative operators (Lee-Wick operators) to its action. The effects of these operators are investigated both at the classical and quantum levels.
We show that the source of RR field computed from the boundary state describing the decay of a non-BPS brane is reproduced by a particular form of the Wess-Zumino term in the tachyon effective action. We also obtain a simple expression of the S-charge associated with rolling tachyons.
We construct noncommutative extension of the Wess-Zumino-Witten (WZW) model and study its ultraviolet property. The β-function of the U(N) noncommutative WZW model resembles that of the ordinary WZW model. The U(1) noncommutative model has also a nontrivial fixed point.
These lecture notes are a brief introduction to Wess-Zumino-Witten models, and their current algebras, the affine Kac-Moody algebras. After reviewing the general background, we focus on the application of representation theory to the computation of 3-point functions and fusion rules.
We study the phase diagram of the two-dimensional N=1 Wess-Zumino model on the lattice using Wilson fermions and the fermion loop formulation. We give a complete nonperturbative determination of the ground state structure in the continuum and infinite volume limit. We also present a determination of the particle spectrum in the supersymmetric phase, in the supersymmetry broken phase and across the supersymmetry breaking phase transition. In the supersymmetry broken phase we observe the emergence of the Goldstino particle.
It is shown that canonical quantization of the $4d$ Siegel superparticle yields massless Wess-Zumino model as an effective field theory. Quantum states of the superparticle are realized in terms of the real scalar superfields which prove to be decomposed into the sum of on-shell chiral and antichiral superfields.
We study the effective action associated to the Dirac operator in two dimensional non-commutative Field Theory. Starting from the axial anomaly, we compute the determinant of the Dirac operator and we find that even in the U(1) theory, a Wess-Zumino-Witten like term arises.
We analyze the connection between Wess-Zumino-Witten and free fermion models in two-dimensional noncommutative space. Starting from the computation of the determinant of the Dirac operator in a gauge field background, we derive the corresponding bosonization recipe studying, as an example, bosonization of the U(N) Thirring model. Concerning the properties of the noncommutative Wess-Zumino-Witten model, we construct an orbit-preserving transformation that maps the standard commutative WZW action into the noncommutative one.
We consider the open superstring action in AdS_5 x S^5 background with the bilinear Wess-Zumino term, which has been modified in such a way that a certain total derivative term is absent, and give the covariant description of supersymmetric D-branes. We show that the modification of bilinear Wess-Zumino term is necessary to describe correctly the 1/2-BPS D(-1)-brane in AdS_5 x S^5 background, while the classification of other supersymmetric D-branes does not depend on such modification.
General expressions for the anomalies appearing in pure W_3 gravity are found by requiring that they satisfy a modified version of the Wess-Zumino consistency conditions in which the Ward identities are treated as nonvanishing quantities.
We propose an effective action that describe a relativistic fluid with Hall viscosity. The construction involves a Wess-Zumino-Witten term that exists only in (2+1) spacetime dimensions. We note that this formalism can accommodate only a Hall viscosity which is a homogeneous function of the entropy and particle number densities of degree one.
We prove that the equations of motion describing domain walls in a Wess-Zumino theory involving only one chiral matter multiplet can be factorized into first order Bogomol'nyi equations, so that all the topological defects are of the Bogomol'nyi-Prasad-Sommerfield type.
The Wess-Zumino term is constructed for supersymmetric QCD with two colors and flavors, and is shown to correctly reproduce the anomalous Ward identities. Supersymmetric QCD is also shown not to have topologically stable skyrmion solutions because of baryon flat directions, which allow them to unwind. The generalization of these results to other supersymmetric theories with quantum modified constraints is discussed.
We consider the non-interacting massive Wess-Zumino model in four-dimensional anti-de Sitter space and show that the conformal dimensions of the corresponding boundary fields satisfy the relations expected from superconformal invariance. In some cases the irregular mode must be used for one of the scalar fields.
A consistent quantization procedure of anomalous chiral models is discussed. It is based on the modification of the classical action by adding Wess-Zumino terms. The $SO(3)$ invariant WZ action for the $SO(3)$ model is constructed. Quantization of the corresponding modified theory is considered in details.
As a contribution to the current efforts to understand supersymmetry-breaking by meta-stable vacua, we study general properties of supersymmetry-breaking vacua in Wess-Zumino models: we show that tree-level degeneracy is generic, explore some constraints on the couplings and present a simple model with a long-lived meta-stable vacuum, ending with some generalizations to non-renormalizable models.
In this paper we give some prescriptions in order to remove the Wess Zumino fields of the BFFT formalism and, consequently, we derive a gauge invariant system written only in terms of the original second class phase space variables. Here, the Wess Zumino fields are considered only as auxiliary variables that permit us to reveal the underlying symmetries present in a second class system. We apply our formalism in three important and illustrative constrained systems which are the Chern Simons Proca theory, the Abelian Proca model and the reduced SU(2) Skyrme model.
The background for string propagation is obtained by a chiral gauging of the $SL(2,R)$ Wess-Zumino-Witten model. It is shown explicitly that the resulting background fields satisfy the field equations of the three dimensional string effective action and the target space has curvature singularity. Close connection of our solution with the three dimensional black string is demonstrated.
In the relation between the linear (L) supersymmetry (SUSY) representation and the nonlinear (NL) SUSY representation we discuss the role of the Wess-Zumino gauge. We show in two dimensional spacetime that a spontaneously broken LSUSY theory with mass and Yukawa interaction terms for a minimal off-shell vector supermultiplet is obtained from a general superfield without imposing any special gauge conditions in N = 2 NL/L SUSY relation.
In this letter we use the spurion field approach adopted in hep-th/0307099 in order to show that by adding F and F^2 terms to the original lagrangian, the N=1/2 Wess-Zumino model is renormalizable to all orders in perturbation theory. We reformulate in superspace language the proof given in the recent work hep-th/0307165 in terms of component fields.
We introduce the notion of superoperators on noncommutative R^4 and re-investigate in the framework of superfields the noncommutative Wess-Zumino model as a quantum field theory. In a highly efficient manner we are able to confirm the result that this model is renormalizable to all orders.
A new way of solving the descent equations corresponding to the Wess-Zumino consistency conditions is presented. The method relies on the introduction of an operator $δ$ which allows to decompose the exterior space-time derivative $d$ as a $BRS$ commutator. The case of the Yang-Mills theories is treated in detail.
We consider the 2--dimensional Wess--Zumino--Witten (WZW) model in the canonical formalism introduced in a previous paper by two of us. Using an $r$--$s$ matrix approach to non--ultralocal field theories we find the Poisson algebra of monodromy matrices and of conserved quantities with a new, non--dynamical, $r$ matrix.
We investigate the Kac-Moody algebra of noncommutative Wess-Zumino-Witten model and find its structure to be the same as the commutative case. Various kinds of gauged noncommutative WZW models are constructed. In particular, noncommutative $U(2)/U(1)$ WZW model is studied and by integrating out the gauge fields, we obtain a noncommutative non-linear $σ$-model.
Reducible off-shell anomalous gauge theories are studied in the framework of an extended Field-Antifield formalism by introducing new variables associated with the anomalous gauge degrees of freedom. The Wess-Zumino term for these theories is constructed and new gauge invariances appear. The quantum effects due to the extra variables are considered.
An exact conformal field theory describing a four dimensional 2-brane solution is found by considering a chiral gauged Wess-Zumino -Witten theory corresponding to $SL(2, R)\times R$ , where one gauges the one dimensional $U(1)$ subgroup together with a translation in $R$. The backgrounds for string propagation are explicitly obtained and the target space is shown to have a true curvature singularity.
We look at the equivalence of the massive Thirring and sine-Gordon models. Previously, this equivalence was derived perturbatively in mass (though to all orders). Our calculation goes beyond that and uncovers an underlying conformal symmetry.
Using a superfield generalization of the tadpole method, we study the one-loop effective potential for a Wess Zumino model modified by a higher-derivative term, inspired by the Lee-Wick model. The one-loop Kählerian potential is also obtained by other methods and compared with the effective potential.
By explicit calculation, we show that the expansion of the disk level S-matrix element of one RR field, two open string tachyons and one gauge field that has been recently found corresponds to the derivative expansion of the Wess-Zumino action of D-brane-anti-D-brane systems.
We derive an exact expression for the tachyon $β$-function for the Wess-Zumino-Witten model. We check our result up to three loops by calculating the three-loop tachyon $β$-function for a general non-linear $σ$-model with torsion, and then specialising to the case of the WZW model.
The spectrum of supersymmetric domain wall solitons of the Wess-Zumino model is known to be discontinuous across a curve (of marginal stability) in the moduli space of quartic superpotentials. Here we show how this phenomenon can be understood from the behavior of the long-range inter-soliton force, which we compute by a method due to Manton.
We perform the group analysis of Witten's equations of motion for a particle moving in the presence of a magnetic monopole, and also when constrained to move on the surface of a sphere, which is the classical Wess-Zumino-Witten model. We also consider variations of this model. Our analysis gives the generators of the corresponding Lie point symmetries. The Lie symmetry corresponding to Kepler's third law is obtained in two related examples.
We reconstruct the action of $N=1, D=4$ Wess-Zumino and $N=1, 2, D=4$ super-Yang-Mills theories, using integral top forms on the supermanifold ${\cal M}^{(4|4)}$. Choosing different Picture Changing Operators, we show the equivalence of their rheonomic and superspace actions. The corresponding supergeometry and integration theory are discussed in detail. This formalism is an efficient tool for building supersymmetric models in a geometrical framework.
The Wess-Zumino model on N=1/2 nonanticommutative superspace, which contains the dimension-6 term F^3, is shown to be renormalizable to all orders in perturbation theory, upon adding F and F^2 terms to the original Lagrangian. The renormalizability is possible, even with this higher-dimension operator, because the Lagrangian is not hermitian. Such deformed field theories arise naturally in string theory with a graviphoton background.
We consider the abelian vector-field models in the presence of the Wess-Zumino interaction with the pseudoscalar matter. The occurence of the dynamic breaking of Lorentz symmetry at classical and one-loop level is described for massless and massive vector fields. This phenomenon appears to be the non-perturbative counterpart of the perturbative renormalizability and/or unitarity breaking in the chiral gauge theories.
