Wess-Zumino Term Research Articles

Gauging the SU(2) Skyrme model

In this paper the SU(2) Skyrme model will be reformulated as a gauge theory and the hidden symmetry will be investigated and explored in the energy spectrum computation. To this end we propose a constraint conversion scheme, based on the symplectic framework with the introduction of Wess-Zumino terms in an unambiguous way. It is a positive feature not present in the Batalin-Fradkin-Fradkina-Tyutin constraint conversion. Dirac's procedure for the first-class constraints is employed to quantize this gauge-invariant nonlinear system and the energy spectrum is computed. The result shows the power of the symplectic gauge-invariant formalism when compared with other constraint conversion procedures present in the literature.

D-branes in non-tachyonic 0B orientifolds

We determine all D-branes in the non-tachyonic 0'B orientifold, examine their worldvolume anomalies and study orbifold compactifications. We find that the spectrum of the D-branes contains chiral fermions in the symmetric, antisymmetric and fundamental representations of (unitary) gauge groups on the branes. The cancellation of the worldvolume anomalies requires Wess–Zumino terms which we determine explicitly. We examine a non-tachyonic compactification to 9d whose closed part interpolates between 0B and IIB and revisit compactifications on orbifolds. The D3-brane allows to conjecture, via the AdS/CFT correspondence, a supergravity dual to a non-supersymmetric and infrared-free gauge theory. The D-string gives hints concerning the S-dual of the 0'B orientifold.

Derivative corrections to D-brane actions with constant background fields

We study derivative corrections to the effective action for a single D-brane in type II superstring theory coupled to constant background fields. In particular, within this setting we determine the complete expression for the (disk level) four-derivative corrections to the Born-Infeld part of the action. We also determine 2n-form 2n-derivative corrections to the Wess-Zumino term. Both types of corrections involve all orders of the gauge field strength, F. The results are obtained via string sigma-model loop calculations using the boundary state operator language. The corrections can be succinctly written in terms of the Riemann tensor for a non-symmetric metric.

Superstrings and superbranes with a modified measure

For superstrings, the consequences of replacing the measure of integration $\sqrt{-\gamma}d^2 x$ in the Polyakov's action by $\Phi d^2 x$ where $\Phi$ is a density built out of degrees of freedom independent of the metric $\gamma_{ab}$ defined in the string are studied. As in Siegel reformulation of the Green Schwarz formalism the Wess-Zumino term is the square of supersymmetric currents. As opposed to the Siegel case, the compensating fields needed for this do not enter into the action just as in a total derivative. They instead play a crucial role to make up a consistent dynamics. The string tension appears as an integration constant of the equations of motion. The generalization to higher dimensional extended objects is also studied using in this case the Bergshoeff and Sezgin formalism with the associated additional fields, which again are dynamically relevant unlike the standard formulation. Also unlike the standard formulation, there is no need of a cosmological term on the world brane.

Hamilton-Jacobi Treatment of Chiral Schwinger Model

We investigate the path integral quantization of the bosonic chiral Schwinger model using multi-Hamilton–Jacobi procedure. The integrability conditions require the extension of the initial phase space. The Wess–Zumino term was recovered calculating the action corresponding to the extended system.

Skyrmions from SU(3) harmonic maps and their quantization

Static properties of SU(3) multiskyrmions with baryon numbers up to 6 are estimated. The calculations are based on the recently suggested generalization of the SU(2) rational map ansätze applied to the SU(3) model. Both SU(2) embedded skyrmions and genuine SU(3) solutions are considered and it is shown that although, at the classical level, the energy of the embeddings is lower, the quantum corrections can alter these conclusions. This correction to the energy of the lowest state, depending on the Wess–Zumino term, is presented in the most general case.

Wess–Zumino terms and duality

We show the equivalence between Stückelberg and Wess–Zumino methods of restoration of gauge symmetries of the anomalous, Abelian, effective action, in arbitrary even dimensions D=2 k. We present dual version of Wess–Zumino terms with the compensating field described by a Kalb Ramond like p=2 k−2 form.

Anomaly matching and a Hopf–Wess–Zumino term in six-dimensional, field theories

We point out that the low energy theory of 6d, N=(2,0) field theories, when away from the origin of the moduli space of vacua, necessarily includes a new kind of Wess-Zumino term. The form of this term is related to the Hopf invariant associated with \pi_7 (S^4). The coefficient of the Wess-Zumino term is fixed by an anomaly matching relation for a global flavor symmetry. For example, in the context of a single M5 brane probe in the background of N distant M5 branes, the probe must have the Hopf-WZ term with coefficient proportional to N(N+1). Various related checks and observations are made. We also point out that there are skyrmionic strings, and propose that they are the W-boson strings.

Conserved charges and supersymmetry in principal chiral and WZW models

Conserved and commuting charges are investigated in both bosonic and supersymmetric classical chiral models, with and without Wess-Zumino terms. In the bosonic theories, there are conserved currents based on symmetric invariant tensors of the underlying algebra, and the construction of infinitely many commuting charges, with spins equal to the exponents of the algebra modulo its Coxeter number, can be carried out irrespective of the coefficient of the Wess-Zumino term. In the supersymmetric models, a different pattern of conserved quantities emerges, based on antisymmetric invariant tensors. The current algebra is much more complicated than in the bosonic case, and it is analysed in some detail. Two families of commuting charges can be constructed, each with finitely many members whose spins are exactly the exponents of the algebra (with no repetition modulo the Coxeter number). The conserved quantities in the bosonic and supersymmetric theories are only indirectly related, except for the special case of the WZW model and its supersymmetric extension.

Wess-Zumino terms for the deformed Skyrme model

A formulation of Skyrme model as an embedded gauge theory with the constraint deformed away from the spherical geometry is proposed. The gauge invariant formulation is obtained firstly generalizing the intrinsic geometry of the model and then converting the constraint to first-class through an iterative Wess-Zumino procedure. The gauge invariant model is quantized via Dirac method for first-class system. A perturbative calculation provides new free parameters related to deformation that improve the energy spectrum obtained in earlier approaches.

Resonant quantum coherence of magnetization at excited states in nanospin systems with different crystal symmetries

The quantum interference effects induced by the Wess-Zumino term, or Berry phase are studied theoretically in resonant quantum coherence of magnetization vector between degenerate excited states in nanometer-scale single-domain ferromagnets in the absence of an external magnetic field. By applying the periodic instanton method in the spin-coherent-state path integral, we evaluate the low-lying tunnel splittings between degenerate excited states of neighboring wells. And the low-lying energy level spectrum of m-th excited states are obtained with the help of the Bloch theorem in one-dimensional periodic potential.

Supersymmetric brane-worlds

We present warped metrics which solve Einstein equations with arbitrary cosmological constants in both in upper and lower dimensions. When the lower-dimensional metric is the maximally symmetric one compatible with the chosen value of the cosmological constant, the upper-dimensional metric is also the maximally symmetric one and there is maximal unbroken supersymmetry as well. We then introduce brane sources and find solutions with analogous properties, except for supersymmetry, which is generically broken in the orbifolding procedure (one half is preserved in two special cases), and analyze metric perturbations in these backgrounds In analogy with the D8-brane we propose an effective ( d ̂ −2) -brane action which acts as a source for the RS solution. The action consists of a Nambu–Goto piece and a Wess–Zumino term containing a ( d ̂ −1) -form field. It has the standard form of the action for a BPS extended object, in correspondence with the supersymmetry preserved by the solution.

Triplectic quantization ofW2gravity

The role of one loop order corrections in the triplectic quantization is discussed in the case of W2 theory. This model illustrates the presence of anomalies and Wess Zumino terms in this quantization scheme where extended BRST invariance is represented in a completely anticanonical form.

Type II branes from brane–antibrane in M-theory

We discuss in a systematic way all the possible realisations of branes of M and type II theories as topological solitons of a brane–antibrane system. The classification of all the possibilities, consistent with the structure of the theory, is achieved by studying the Wess–Zumino terms in the worldvolume effective actions of the branes of M-theory and their reductions.

IIB-branes and new spacetime superalgebras

We provide a classification of the IIB D$p$- and NS$p$-branes in which the brane action exists due to a non-trivial class of the Chevalley-Eilenberg cohomology of free differential algebras. We then present a new geometric formulation of the IIB D$p$- and NS$p$-branes ($p\leq 5$) in which the manifestly superinvariant Wess-Zumino terms are constructed in terms of the supersymmetric currents. The supercurrents are obtained by using supergroup manifolds corresponding to the IIB-brane superalgebra, which is characterized by the generators of D3-, D5-, NS5- and KK5-branes in addition to the previously introduced generators of supertranslations, F- and D-strings. The charges of D1-, F1- and D3-branes are related to those of the M-algebra, but some charges of D5- and NS5-branes are not. The S-duality of the type-IIB theory is realized as transformations of the supercurrents generalizing the SO(2) R-symmetry of the superalgebra. We thus find that the superalgebra is lifted into twelve-dimensions with signature (11,1).

Induced charge matching and Wess-Zumino term on quantum modified moduli space

Recently it was proposed that matching of global charges induced in vacuum by slowly varying, topologically non-trivial scalar fields provides consistency conditions analogous to the 't Hooft anomaly matching conditions. We study matching of induced charges in supersymmetric $\mathrm{SU}(N)$ gauge theories with quantum modified moduli space. We find that the Wess-Zumino term should be present in the low energy theory in order that these consistency conditions are satisfied. We calculate the lowest homotopy groups of the quantum moduli space, and show that there are no obstructions to the existence of the Wess-Zumino term at arbitrary N. The explicit expression for this term is given. It is shown that neither vortices nor topological solitons exist in the model. The case of softly broken supersymmetry is considered as well. We find that the possibility of the global flavor symmetric vacuum is strongly disfavored.

Magnetic interactions of D-branes and Wess-Zumino terms in Super Yang-Mills effective actions

There is a close relation between classical supergravity and quantum SYM descriptions of interactions between separated branes. In the case of D3 branes the equivalence of leading-order potentials is due to non-renormalization of the F 4 term in N=4 SYM theory. Here we point out the existence of another special non-renormalized term in quantum SYM effective action. This term reproduces the interaction potential between electric charge of a D3-brane probe and magnetic charge of a D3-brane source, represented by the Chern-Simons part of the D-brane action. This unique Wess-Zumino term depends on all six scalar fields and originates from a phase of the euclidean fermion determinant in SYM theory. It is manifestly scale invariant (i.e. is the same for large and small separations between branes) and can not receive higher loop corrections in gauge theory. Maximally supersymmetric SYM theories in D= p+1>4 contain mixed WZ terms which depend on both scalar and gauge field backgrounds, and which reproduce the corresponding CS terms in the supergravity interaction potentials between separated Dp-branes for p>3. Purely scalar WZ terms appear in other cases, e.g., in half less supersymmetric gauge theories in various dimensions describing magnetic interactions between D p and D(6− p) branes.

Tduality and effective D-brane actions

$T$ duality realized on D-brane effective actions is studied from a pure worldvolume point of view. It is proved that invariance in the form of the Dirac-Born-Infeld and Wess-Zumino terms fixes the T-duality transformations of the $\mathrm{NS}\ensuremath{-}\mathrm{NS}$ and $R\ensuremath{-}R$ background fields, respectively. The analysis is extended to uncover the mapping of global symmetries of the corresponding pair of D-branes involved in the transformation.

The Wess–Zumino term and quantum tunneling

The significance of the Wess–Zumino term in spin tunneling is explored, and a formula is established for the splitting of energy levels of a particle with large fermionic spin as an applied magnetic field is switched on.

AdS calibrations

We present a new bound for the worldvolume actions of branes with a Wess-Zumino term. For this we introduce a generalization of calibrations for which the calibration form is not closed. We then apply our construction to find the M-5-brane worldvolume solitons in an AdS background that saturate this bound. We show that these worldvolume solitons are supersymmetric and that they satisfy differential equations which generalize those of standard calibrations.