A large class of integrable deformations of the Principal Chiral Model, known as the Yang-Baxter deformations, are governed by skew-symmetric R-matrices solving the (modified) classical Yang-Baxter equation. We carry out a systematic investigation of these deformations in the presence of the Wess-Zumino term for simple Lie groups, working in a framework that treats both inhomogeneous and homogeneous deformations on the same footing. After analysing the cohomological conditions under which such a deformation is admissible, we consider an action for the general Yang-Baxter deformation of the Principal Chiral Model plus Wess-Zumino term and prove its classical integrability. We also show how the model is found from a number of alternative formulations: affine Gaudin models, E-models, 4-dimensional Chern-Simons theory and, for homogeneous deformations, non-abelian T-duality.
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.
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 consider the effective potential V in the massless Wess-Zumino model. By using the renormalization group equation, we show that the explicit dependence of V on the renormalization mass scale mu cancels. If V has an extremum at some non-vanishing value of the background field, then it follows that V is "flat", independent of the background field. This is consistent with the general requirement that V be complex. The consequences for supersymmetric gauge theories are briefly considered.
In our previous paper we construct a renormalizable Wess-Zumino action on BFNC superspace at the second order approximation of noncommutative parameters. The action contains about 200 terms which are necessary for renormalization. By removing chiral covariant derivatives and chiral coordinates we found that the BFNC Wess-Zumino action can be transformed to a simpler form which have manifest 1/2 supersymmetry. Based on this discovery, we can extend the BFNC Wess-Zumino action to the all order of noncommutative parameters. At first we introduce global symmetries, then obtain divergent operators …
We consider a Galilean N=2 supersymmetric theory in 2+1 dimensions with F-term couplings, obtained by null reduction of a relativistic Wess-Zumino model. We compute quantum corrections and we check that, as for the relativistic parent theory, the F-term does not receive quantum corrections. Even more, we find evidence that the causal structure of the non-relativistic dynamics together with particle number conservation constrain the theory to be one-loop exact.
Using numerical bootstrap method, we determine the critical exponents of the minimal three-dimensional N = 1 Wess-Zumino models with cubic superpotetential $W\sim d_{ijk}Φ_iΦ_jΦ_k$. The tensor $d_{ijk}$ is taken to be the invariant tensor of either permutation group $S_N$, special unitary group $SU(N)$, or a series of groups called F4 family of Lie groups. Due to the equation of motion, at the Wess-Zumino fixed point, the operator $d_{ijk}Φ_iΦ_jΦ_k$ is a (super)descendant of $Φ_i$ . We observe such super-multiplet recombination in numerical bootstrap, which allows us to determine the scaling d…
We continue the study of the gl(1|1) Wess-Zumino-Witten model. The Knizhnik-Zamolodchikov equations for the one, two, three and four point functions are analyzed, for vertex operators corresponding to typical and projective representations. We illustrate their interplay with the logarithmic global conformal Ward identities. We compute the four point function for one projective and three typical representations. Three coupled first order Knizhnik-Zamolodchikov equations are integrated consecutively in terms of generalized hypergeometric functions, and we assemble the solutions into a local corr…
