Wess-Zumino Term Research Articles

Conformally gauge-fixed Polyakov D1-brane action in the presence of a 2-form gauge field: the instant-form and front-form Hamiltonian and path integral formulations

The conformally gauge-fixed Polyakov D1-brane action (CGFPD1BA) describing a gauge-noninvariant (GNI) theory (being a gauge-fixed theory) is seen to describe a gauge-invariant (GI) theory in the presence of an antisymmetric 2-form gauge field Bαβ.The 2-form gauge field is seen to behave like a Wess–Zumino (WZ) field and the term involving this field is seen to behave like a WZ term for the CGFPD1BA. In this Letter we investigate the instant-form and front-form Hamiltonian and path integral formulations of this GI theory describing the CGFPD1BA in the presence of a constant 2-form gauge-field, in the absence of boundary conditions, under appropriate gauge-fixing conditions.

Hamiltonian and BRST formulations of a gauge-invariant chiral Schwinger model with the Faddeevian regularization

The Hamiltonian and BRST formulations of a gauge-invariant chiral Schwinger model with the Faddeevian regularization due to Mukhopadhyay and Mitra in one-space one-time dimensions (obtained by the inclusion of an appropriate Wess–Zumino term in the action of the originally gauge-noninvariant model due to Mitra) are investigated under some specific gauge choices in the usual instant form of dynamics (on the hyperplanes x0= constant). The physical contents of the original gauge-noninvariant theory are recovered from that of this gauge-invariant theory under a special choice of gauge, and the quantum equivalence of the two quantized theories is established.PACS Nos.: 03.65+, 03.70+, 11.10lm, 11.10Ef, and 11.30Rd

Gauge-invariant action for superstring in Ramond–Ramond plane-wave background

We present an alternative form of gauge-invariant action for the superstring in the plane wave background with Ramond–Ramond (RR) five-form flux. The Wess–Zumino term is given explicitly in a bilinear form of the left-invariant currents by introducing a fermionic center to define the nondegenerate group metric. The reparametrization invariance generators, whose combinations are conformal generators, and fermionic constraints, half of which generate κ-symmetry, are obtained. Equations of motion are obtained in conformal-invariant and background-covariant manners.

Wess-Zumino term for AdS superstring

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.

An Inverse Penrose Limit and Supersymmetry Enhancement in the Presence of Tensor Central Charges

A connection between weak and strong tension limits and their perturbative corrections is discussed. New twistor-like models based on D=4, N=1 tensionless superstring and superbrane with tensor central charges are studied. The presence of three, two or less preserved fractions of $\kappa-$symmetry in the actions free of the Wess-Zumino terms is shown. A correlation of extra $\kappa-$symmetry with the R-symmetry is established. The equations of the superstring and superbrane models preserving 3/4 supersymmetry are exactly solved. The general solution for the Goldstone fermion is pure static, but for the Goldstone bosons it also includes a term describing string/brane motions along the fixed directions given by the initial data. These solutions correspond to the partial spontaneous breaking of the D=4, N=1 global supersymmetry and can be associated with a static closed magnetic Nielsen-Olesen vortex or a p-dimensional vortex.

Antiperiodic wave functions of Schrödinger cat states for nano-magnets and the realization of macroscopic Fermi-particles

The point-particle-like Hamiltonian of a biaxial nano-magnet is obtained in terms of the potential field description of quantum spins with exact spin coordinate correspondence. We demonstrate that the quenching of macroscopic quantum coherence (MQC) investigated in terms of the distractive topological phase interference of tunneling paths can be resulted directly from the antiperiodic wave functions of Schrödinger cat states of the nano-particle and is therefore regarded as the realization of a macroscopic Fermi-particle. We also prove the equivalence between the antiperiodic boundary condition of the wave function and the Wess–Zumino term in Lagrangian which leads to the topological phase of tunneling paths.

Quantum mechanics of a superparticle with 1/4 supersymmetry breaking

We study quantum mechanics of a massive superparticle in $d=4$ which preserves 1/4 of the target space supersymmetry with eight supercharges, and so corresponds to the partial breaking $N=\stackrel{\ensuremath{\rightarrow}}{8}N=2.$ Its worldline action contains a Wess-Zumino term, explicitly breaks $d=4$ Lorentz symmetry and exhibits one complex fermionic $\ensuremath{\kappa}$ symmetry. We perform the Hamiltonian analysis of the model and quantize it in two different ways: with gauge-fixed $\ensuremath{\kappa}$ symmetry and in the Gupta-Bleuler formalism. Both approaches give rise to the same supermultiplet structure of the space of states. It contains three irreducible $N=2$ multiplets with the total number of $(4+4)$ complex on-shell components. These states prove to be in one-to-one correspondence with the de Rham complex of p-forms on a three-dimensional subspace of the target x manifold. We analyze the vacuum structure of the model and find that the nontrivial vacua are given by the exact harmonic one- and two-forms. Despite the explicit breaking of $d=4$ Lorentz symmetry in the fermionic sector, the $d=4$ mass-shell condition is still valid in the model.

Localized fermions and anomaly inflow via deconstruction

We study fermion localization in gauge theory space. We consider four-dimensional product gauge groups in which light chiral fermions transform under different gauge factors of the product group. This construction provides a suppression of higher dimensional operators. For example, it can be used to suppress dangerous proton decay operators. The anomalies associated with the light chiral fermions are compensated by Wess-Zumino terms, which in the continuum limit reproduce the five-dimensional Chern-Simons term.

D-branes, fluxes and chirality

We describe a topological effect on configurations of D-branes in the presence of NS-NS and RR field strength fluxes. The fluxes induce the appearance of chiral anomalies on lower dimensional submanifolds of the D-brane worldvolume. This anomaly is not associated to a dynamical chiral fermion degree of freedom, but rather should be regarded as an explicit flux-induced anomalous term (Wess-Zumino term) in the action. The anomaly is cancelled by an inflow mechanism, which exploits the fact that fluxes can act as sources of RR fields. We discuss several applications of this flux-induced anomaly; among others, its role in understanding anomaly cancellation in compactifications with D-branes and fluxes, and the possibility of phase transitions where a chiral fermion disappears from the D-brane world-volume spectrum, being replaced by an explicit Wess-Zumino term. We comment on the relation among different mechanisms to obtain four-dimensional chirality in string theory.

EFFECTIVE THEORY FOR A QUANTUM SPIN SYSTEM IN LOW DIMENSIONS – BEYOND THE LONG WAVELENGTH LIMIT

An effective theory for a quantum spin system in low dimensions is constructed in the finite-q regime. It is shown that there are field configurations for which Wess–Zumino terms contribute to the partition functions as topological terms for ferromagnets as well as antiferromagnets in both one- and two-dimensional lattices. This is in sharp contrast to the absence of topological excitations in two-dimensional quantum antiferromagnets in the long wavelength limit.

The Wess-Zumino term for a harmonic map

We calculate the Wess-Zumino term $\Gamma(g)$ for a harmonic map $g$ of a closed surface to a compact, simply connected, simple Lie group $G$ in terms of the energy and the holonomy of the Chern-Simons line bundle on the moduli space of flat $G$-connections. In the case of the 2-sphere we deduce that $\Gamma(g)$ is 0 or $\pi$ and for the 2-torus and $G=SU(2)$ we give a formula involving hyperelliptic integrals.

Gravitational couplings of orientifold planes

We reanalyse the gravitational couplings of the perturbative orientifold planes $Op^-$, $Op^+$ (and D-branes). We first compute their $D_{-1}$ instantonic corrections for $p=3$. Then, by using U-dualities, we obtain the Wess-Zumino terms of orientifolds with RR flux for $p \leq 5$. The expressions for the effective actions can be partially checked via M-theory. We point out a previous oversimplification and we show in fact that the difficulty still stands in the way of the full computation of 7 Brane instanton corrections.

Geometry of quaternionic Kähler connections with torsion

The target space of a (4,0) supersymmetric two-dimensional sigma model with Wess–Zumino term has a connection with totally skew-symmetric torsion and holonomy contained in SP( n)·SP(1), QKT connection. We study the geometry of QKT connections. We find conditions to the existence of a QKT connection and prove that if it exists it is unique. We show that QKT geometry persist in a conformal class of metrics which allows us to obtain a lot of (compact) examples of QKT manifolds. We present a (local) description of four-dimensional homogeneous QKT structures relying on the known result of naturally reductive homogeneous Riemannian manifolds. We consider Einstein-like QKT manifold and find closed relations with Einstein–Weyl geometry in dimension 4.

Boundary G/G theory and topological Poisson-Lie sigma model

We study a boundary version of the gauged WZW model with a Poisson–Lie group G as the target. The Poisson–Lie structure of G is used to define the Wess–Zumino term of the action on surfaces with boundary. We clarify the relation of the model to the topological Poisson sigma model with the dual Poisson–Lie group G* as the target and show that the phase space of the theory on a strip is essentially the Heisenberg double of G introduced by Semenov–Tian–Shansky.

NONCOMMUTATIVE GEOMETRY, GEOMETRICAL ASPECTS OF SKYRMIONS AND STRING THEORY

It is pointed out here that noncommutative geometry having the space–time manifold X = M4× Z2leads to the description of a massive fermion as a skyrmion when the discrete space–time is incorporated as an internal variable. The inherent anisotropic feature of the internal space gives rise to the Skyrme term as well as the Wess–Zumino term. An array of such skyrmions may be considered as a three-dimensional Ising system. It is shown that the composite system of such skyrmions may be viewed as the (3 + 1)-dimensional relative of the Polyakov string theory when the associated Liouville field corresponds to the attachment of topological fixtures like vortex lines at the end points of an open string. These two systems are found to satisfy certain duality principles through conformal duality which are similar to T duality and S duality in conventional string picture.

Topology of the quantum modified moduli space

Abstract We study the topology of the quantum space of vacua in N = 1 SQCD with Nf = Nc. We show that no topological solitons exist in the model. On the other hand, the Wess-Zumino term can be constructed. Then we consider orbifold projection in this model. We show that topological solitons appear in the projected theory. Their presence may be crucial for the commutativity of the orbifold projection and the infrared limit, provided the solitons become massless in the large Nc limit.

Geometric couplings and brane supersymmetry breaking

Orientifold vacua allow the simultaneous presence of supersymmetric bulks, with one or more gravitinos, and nonsupersymmetric combinations of BPS branes. This “brane supersymmetry breaking” raises the issue of consistency for the resulting gravitino couplings, and Dudas and Mourad recently provided convincing arguments to this effect for the ten-dimensional USp(32) model. These rely on a nonlinear realization of local supersymmetry à la Volkov–Akulov, although no gravitino mass term is present, and the couplings have a nice geometrical interpretation in terms of “dressed” bulk fields, aside from a Wess–Zumino-like term, resulting from the supersymmetrization of the Chern–Simons couplings. Here we show that all couplings can be given a geometrical interpretation, albeit in the dual 6-form model, whose bulk includes a Wess–Zumino term, so that the nongeometric ones are in fact demanded by the geometrization of their duals. We also determine the low-energy couplings for six-dimensional (1,0) models with brane supersymmetry breaking. Since these include both Chern–Simons and Wess–Zumino terms, only the resulting field equations are geometrical, aside from contributions due to vectors of supersymmetric sectors.

New remarks on the linear constraint self-dual boson and Wess-Zumino terms

In this work we prove in a precise way that the soldering formalism can be applied to the Srivastava chiral boson (SCB), in contradiction with some results appearing in the literature. We have promoted a canonical transformation that shows directly that the SCB is composed of two Floreanini-Jackiw's particles with the same chirality which spectrum is a vacuum-like one. As another conflictive result we have proved that a Wess-Zumino term used in the literature consists of the scalar field, once again denying the assertion that the WZ term adds a new degree of freedom to the SCB theory in order to modify the physics of the system.

Dielectric D0-branes in near-horizon D-brane backgrounds and D-strings under electric RR fluxes

Using the nonabelian Dirac–Born–Infeld action with the Wess–Zumino term that is constructed in consistent with T duality we examine the Myers dielectric effect for multiple D0-branes in the near-horizon geometry of D4-branes. The effect in the curved spacetime is also confirmed by the dual formulation based on the abelian Dirac–Born–Infeld action of a D2-brane. Putting a system of multiple D-strings in the external electric RR five-form flux, we construct a noncommutative funnel-like solution where the D-strings expand into a spherical D3-brane. We discuss the external field dependence of the funnel-like or wormhole solution.

Morita Equivalence of the Dirac-Born-Infeld Theory with Modulus Φ

Based on the canonical quantization of open strings ending on D-branes with a background B field, we construct the open string propagator. We demonstrate the relation between the T duality of the underlying string theory and the Morita equivalence of the interpolating general Dirac-Born-Infeld theory on a noncommutative torus in the nonzero modulus \Phi sector. The general noncommutative Dirac-Born-Infeld action with the Wess-Zumino terms expressed by the background R-R fields is shown to be Morita invariant.