Wess-Zumino Term Research Articles

Dilatons in hidden local symmetry for hadrons in dense matter

With the explicit breaking of scale invariance by the trace anomaly of QCD rephrased in terms of spontaneous breaking, low-energy strong interaction dynamics of dense and/or hot matter can be effectively captured by – in addition to the Nambu–Goldstone bosons and the vector mesons – two dilaton fields, the “soft” field that is locked to chiral symmetry and the “hard” field which remains unaffected by chiral symmetry. The scale anomaly in which the soft component intervenes can be shown to vanish at the chiral transition, while that of the hard component remains broken throughout the QCD sector. We argue for a remarkable role of the “homogeneous Wess–Zumino term” of the form ω μ B μ on the structure of a single baryon as well as dense baryonic matter. The emerging structure of the dense hadronic matter so obtained suggests a chiral symmetry restored but (quark-)confined phase at high density and a possible remedy to the defect found in the structure of holographic dense matter described in string theory.

Conformal current algebra in two dimensions

We construct a non-chiral current algebra in two dimensions consistent with conformal invariance. We show that the conformal current algebra is realized in non-linear sigma-models on supergroup manifolds with vanishing Killing form, with or without a Wess-Zumino term. The current algebra is computed using two distinct methods. First we exploit special algebraic properties of supergroups to compute the exact two- and three-point functions of the currents and from them we infer the current algebra. The algebra is also calculated by using conformal perturbation theory about the Wess-Zumino-Witten point and resumming the perturbation series. We also prove that these models realize a non-chiral Kac-Moody algebra and construct an infinite set of commuting operators that is closed under the action of the Kac-Moody generators. The supergroup models that we consider include models with applications to statistical mechanics, condensed matter and string theory. In particular, our results may help to systematically solve and clarify the quantum integrability of PSU(n|n) models and their cosets, which appear prominently in string worldsheet models on anti-deSitter spaces.

Supertwistors, massive superparticles and κ-symmetry

We consider a D = 4 two-twistor lagrangian for a massive particle that incorporates the mass-shell condition in an algebraic way, and extend it to a two-supertwistor model with N = 2 supersymmetry and central charge identified with the mass. In the purely supertwistorial picture the two D = 4 super twistors are coupled through a Wess-Zumino term in their fermionic sector. We demonstrate how the ?-gauge symmetry appears in the purely supertwistorial formulation and reduces by half the fermionic degrees of freedom of the two supertwistors; a formulation of the model in terms of ?-invariant degrees of freedom is also obtained. We show that the ?-invariant supertwistor coordinates can be obtained by dimensional (D = 6 ? D = 4) reduction from a D = 6 supertwistor. We derive as well by 6 ? 4 reduction the N = 2 D = 4 massive superparticle model with Wess-Zumino term introduced in 1982. Finally, we comment on general superparticle models constructed with more than two supertwistors.

Axion and neutralinos from supersymmetric extensions of the Standard Model with anomalous [formula omitted]'s

We analyze the conditions under which some supersymmetric generalizations of a class of models descending from string theory allow an axion in the physical spectrum, due to the presence of anomalous Abelian gauge interactions. The gauge structure of these constructions involve the Stückelberg supermultiplet and a supersymmetric version of the Wess–Zumino term for anomaly cancellation. While these conditions are not satisfied by the MSSM superpotential, we show that an axion-like particle appears in the spectrum if extra Standard Model singlets are present. We show that the minimal requirements are met by simple superpotentials in which the singlet superfield is charged under the anomalous U(1). The dark matter sector of these models include an axion and several neutralinos with an axino component.

Two-photon contributions to the Rosenbluth cross-section in the Skyrme model

We study two-photon contributions to the elastic electron-nucleon scattering within the Skyrme model. In particular we focus on the role of the anomaly that enters via the Wess-Zumino term and explain how this induces an axial current interaction.

PATH INTEGRAL QUANTIZATION OF THE CHIRAL SCHWINGER MODEL IN BOSONIZED FORM

The development of the Wess–Zumino action or one-cycle is reviewed from the path integral approach. This is related to the occurrence of anomalies in the theory, and generally signifies a breakdown of gauge invariance. The Jackiw–Rajaraman version of the chiral Schwinger model is studied by means of path integrals. It is shown how the model can be made gauge invariant by using a Wess–Zumino term to write a gauge invariant Lagrangian. The model is considered only in bosonized form without any reference to fermions. The constraints are determined. These components are then used to write a path integral quantization for the bosonized form of the model. Some physical quantities and information, in particular, propagators are derived from the path integral.

FLAT CURRENTS OF A GREEN–SCHWARZ SIGMA MODEL ON SUPERCOSET TARGETS WITH ℤ4m GRADING

We construct actions of Green–Schwarz sigma models on supercoset targets with ℤ4m grading whose kinetic terms only contain the target-space bosons. We consider a simple case of such kinetic term and show that there exist a one-parameter family of flat currents of the model by requiring a suitable choice of the Wess–Zumino term. Such flat currents naturally lead to a hierarchy of classical conserved nonlocal charges. We also find that the one-parameter flat currents of the model satisfy equations of motion and the Virasoro constraint. This implies that one can generate a series of classical solutions from an existing one. When m = 1, our model coincides with the well-known model given by Metsaev and Tseytlin on a supercoset PSU (2, 2|4)/[ SO (4, 1) × SO (5)] and similar models.

On effective actions of non-BPS branes and their higher derivative corrections

By calculating various disk level S-matrix elements and studying in details their momentum expansions, we have extracted some of the couplings in tachyon DBI action and Wess–Zumino terms of the non-BPS branes, and their higher derivative corrections. In particular, we have found that there is exact consistency between field theory and string theory tachyon pole of S-matrix element of one RR and three tachyons provided that one takes into account the fact that the tachyon vertex operator in 0 picture to be along the Pauli matrix σ 1 whereas the tachyon in −1 picture to be along the σ 2 direction. This internal CP factors should be included in the tachyon DBI part of the effective action.

Boundary spectra in superspace σ-models

In this note we compute exact boundary spectra for D-instantons in σ-models on the supergroup PSL(2|2). Our results are obtained through an explicit summation of the perturbative expansion for conformal dimensions to all orders in the curvature radius. The analysis exploits several remarkable properties of the perturbation series that arises from rescalings of the metric on PSL(2|2) relative to a fixed Wess-Zumino term. According to Berkovits, Vafa and Witten, the models are relevant in the context of string theory on AdS3 with non-vanishing RR-flux. The note concludes with a number of comments on various possible generalizations to other supergroups and higher dimensional supercoset theories.

Superstrings on AdS4× ℂℙ3as a coset sigma-model

According to the recent proposal by Aharony, Bergman, Jafferis and Maldacena the N=6 supersymmetric Chern-Simons theory in three dimensions has a 't Hooft limit whose holographic dual is described by type IIA superstings on AdS_4 x CP^3 background. We argue that the Green-Schwarz action for type IIA string theory on AdS_4 x CP^3 with kappa-symmetry partially fixed can be understood as a coset sigma-model on the same space supplied with a proper Wess-Zumino term. We construct the corresponding sigma-model Lagrangian and show that it is invariant under a local fermionic symmetry which for generic bosonic string configurations allows one to remove 8 out of 24 fermionic degrees of freedom. The remaining 16 fermions together with their bosonic partners should describe the physical content of AdS_4 x CP^3 superstring. As further evidence, we demonstrate that in the plane-wave limit the quadratic action arising from our model reproduces the one emerging from the type IIA superstring. The coset sigma-model is classically integrable which opens up the possibility to investigate its dynamics in a way very similar to the case of AdS_5 x S^5 superstrings.

Unitarity bounds for gauged axionic interactions and the Green–Schwarz mechanism

We analyze the effective actions of anomalous models in which a four-dimensional version of the Green–Schwarz mechanism is invoked for the cancellation of the anomalies, and we compare it with those models in which gauge invariance is restored by the presence of a Wess–Zumino term. Some issues concerning an apparent violation of unitarity of the mechanism, which requires Dolgov–Zakharov poles, are carefully examined, using a class of amplitudes studied in the past by Bouchiat–Iliopoulos–Meyer (BIM), and elaborating on previous studies. In the Wess–Zumino case we determine explicitly the unitarity bound using a realistic model of intersecting branes (the Madrid model) by studying the corresponding BIM amplitudes. This is shown to depend significantly on the Stückelberg mass and on the coupling of the extra anomalous gauge bosons and allows one to identify standard-model-like regions (which are anomaly-free) from regions where the growth of certain amplitudes is dominated by the anomaly, separated by an inflection point, which could be studied at the LHC. The bound can even be around 5–10 TeV for a Z’ mass around 1 TeV and varies sensitively with the anomalous coupling. The results for the WZ case are quite general and apply to all the models in which an axion-like interaction is introduced as a generalization of the Peccei–Quinn mechanism, with a gauged axion.

Path integration and perturbation theory with complex Euclidean actions

The Euclidean path integral quite often involves an action that is not completely real, i.e. a complex action. This occurs when the Minkowski action contains $t$-odd $CP$-violating terms. This usually consists of topological terms, such as the Chern-Simons term in odd dimensions, the Wess-Zumino term, the $\ensuremath{\theta}$ term or Chern character in 4-dimensional gauge theories, or other topological densities. Analytic continuation to Euclidean time yields an imaginary term in the Euclidean action. It also occurs when the action contains fermions, the fermion path integral being in general a sum over positive and negative real numbers. Negative numbers correspond to the exponential of $i\ensuremath{\pi}$ and hence indicate the presence of an imaginary term in the action. In the presence of imaginary terms in the Euclidean action, the usual method of perturbative quantization can fail. Here the action is expanded about its critical points, the quadratic part serving to define the Gaussian free theory and the higher order terms defining the perturbative interactions. For a complex action, the critical points are generically obtained at complex field configurations. Hence the contour of path integration does not pass through the critical points and the perturbative paradigm cannot be directly implemented. The contour of path integration has to be deformed to pass through the complex critical point using a generalized method of steepest descent, in order to do so. Typically, this procedure is not followed. Rather, only the real part of the Euclidean action is considered, and its critical points are used to define the perturbation theory, a procedure that can lead to incorrect results. In this article we present a simple example to illustrate this point. The example consists of $N$ scalar fields in $0+1$ dimensions interacting with a $U(1)$ gauge field in the presence of a Chern-Simons term. In this example the path integral can be done exactly, the procedure of deformation of the contour of path integration can be done explicitly and the standard method of only taking into account the real part of the action can be followed. We show that the standard method does not give a correct perturbative expansion. The implications of our work include perturbation theory in the standard model which is $CP$-violating, but also for calculations in the presence of topological terms which have given rise to radical changes in the spectrum of the theory.

Ward Identities in the Derivation of Hawking Radiation from Anomalies

Robinson and Wilczek suggested a new method of deriving Hawking radiation by the consideration of anomalies. The basic idea of their approach is that the flux of Hawking radiation is determined by anomaly cancellation conditions in the Schwarzschild black hole (BH) background. Iso et al. extended the method to a charged Reissner-Nordstroem BH and a rotating Kerr BH, and they showed that the flux of Hawking radiation can also be determined by anomaly cancellation conditions and regularity conditions of currents at the horizon. Their formulation gives the correct Hawking flux for all the cases at infinity and thus provides a new attractive method of understanding Hawking radiation. We present some arguments clarifying for this derivation. We show that the Ward identities and boundary conditions for covariant currents without referring to the Wess-Zumino terms and the effective action are sufficient to derive Hawking radiation. Our method, which does not use step functions, thus simplifies some of the technical aspects of the original formulation.

Gauge symmetry in Kitaev-type spin models and index theorems on odd manifolds

We construct an exactly soluble spin- 1 2 model on a honeycomb lattice, which is a generalization of Kitaev model. The topological phases of the system are analyzed by study of the ground state sector of this model, the vortex-free states. Basically, there are two phases, A phase and B phase. The behaviors of both A and B phases may be studied by mapping the ground state sector into a general p-wave paired states of spinless fermions with tunable pairing parameters on a square lattice. In this p-wave paired state theory, the A phase is shown to be the strong paired phase, an insulating phase. The B phase may be either gapped or gapless determined by the generalized inversion symmetry is broken or not. The gapped B is the weak pairing phase described by either the Moore–Read Pfaffian state of the spinless fermions or anti-Pfaffian state of holes depending on the sign of the next nearest neighbor hopping amplitude. A phase transition between Pfaffian and anti-Pfaffian states are found in the gapped B phase. Furthermore, we show that there is a hidden SU(2) gauge symmetry in our model. In the gapped B phase, the ground state has a non-trivial topological number, the spectral first Chern number or the chiral central charge, which reflects the chiral anomaly of the edge state. We proved that the topological number is identified to the reduced eta-invariant and this anomaly may be cancelled by a bulk Wess–Zumino term of SO(3) group through an index theorem in 2 + 1 dimensions.

On Wess–Zumino terms of brane–antibrane systems

We calculate the disk level S-matrix element of one closed string RR field, two open string tachyons and one gauge field in type II superstring theory. An expansion for the S-matrix element has been found that its four leading order terms are reproduced exactly by the symmetric trace tachyon DBI and the Wess–Zumino actions of D-brane–anti-D-brane systems. Using this consistency, we have also found the first higher derivative correction to the some of the WZ terms.

Noncommutative Wess–Zumino–Witten actions and their Seiberg–Witten invariance

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.

Bi-branes: Target space geometry for world sheet topological defects

We establish that the relevant geometric data for the target space description of world sheet topological defects are submanifolds–which we call bi-branes–in the product M 1 × M 2 of the two target spaces involved. Very much like branes, they are equipped with a vector bundle, which in backgrounds with non-trivial B -field is actually a twisted vector bundle. We explain how to define Wess–Zumino terms in the presence of bi-branes and discuss the fusion of bi-branes. In the case of WZW theories, symmetry preserving bi-branes are shown to be biconjugacy classes. The algebra of functions on a biconjugacy class is shown to be related, in the limit of large level, to the partition function for defect fields. We finally indicate how the Verlinde algebra arises in the fusion of WZW bi-branes.

Stückelberg axions and the effective action of anomalous Abelian models. A [formula omitted] model and its signature at the LHC

We elaborate on an extension of the Standard Model with a gauge structure enlarged by a single anomalous U ( 1 ) , where the presence of a Wess–Zumino term is motivated by the Green–Schwarz mechanism of string theory. The additional gauge interaction is anomalous and requires an axion for anomaly cancelation. The pseudoscalar implements the Stückelberg mechanism and undergoes mixing with the standard Higgs sector to render the additional U ( 1 ) massive. We consider a 2-Higgs doublet model. We show that the anomalous effective vertices involving neutral currents are potentially observable. We clarify their role in the case of simple processes such as Z ∗ → γ γ , which are at variance with respect to the Standard Model. A brief discussion of the implications of these studies for the LHC is included.

Stückelberg axions and the effective action of anomalous abelian models 1. A unitarity analysis of the Higgs-axion mixing

We analyze the quantum consistency of anomalous abelian models and of their effective field theories, rendered anomaly-free by a Wess-Zumino term, in the case of multiple abelian symmetries. These models involve the combined Higgs-Stuckelberg mechanism and predict a pseudoscalar axion-like field that mixes with the goldstones of the ordinary Higgs sector. We focus our study on the issue of unitarity of these models both before and after spontaneous symmetry breaking and detail the set of Ward identities and the organization of the loop expansion in the effective theory. The analysis is performed on simple models where we show, in general, the emergence of new effective vertices determined by certain anomalous interactions.

TOPOLOGICAL AND EQUIVALENT MODELS ON BRANE-WORLDS

In this work we obtain topological and equivalent theories on brane-worlds in several dimensions. Our brane is a solitonic-like hypersurface embedded in a spacetime with a specific dimensionality and it appears due to the breaking of a Peccei–Quinn-like symmetry. In the first part of this work, the obtained topological theories are related to a generalization of the axion–photon anomalous interaction in D = 4 (in the Abelian case) and to the Wess–Zumino term (in the non-Abelian case). In the second part, we construct equivalent models on the brane through a mechanism of explicit Lorentz symmetry breaking. The gauge symmetries of such models are discussed within the Stuckelberg formalism.