The Grassmannian-like coset model and the higher spin currents

In the Grassmannian-like coset model, $$ \frac{\mathrm{SU}{\left(N+M\right)}_k}{\mathrm{SU}{(N)}_k\times \mathrm{U}{(1)}_{kNM\left(N+M\right)}} $$ SU N + M k SU N k × U 1 kNM N + M , Creutzig and Hikida have found the charged spin-2, 3 currents and the neutral spin-2, 3 currents previously. In this paper, as an extension of Gaberdiel-Gopakumar conjecture found ten years ago, we calculate the operator product expansion (OPE) between the charged spin-2 current and itself, the OPE between the charged spin-2 current and the charged spin-3 current and the OPE between the neutral spin-3 current and itself for generic N, M and k. From the second OPE, we obtain the new charged quasi primary spin-4 current while from the last one, the new neutral primary spin-4 current is found implicitly. The infinity limit of k in the structure constants of the OPEs is described in the context of asymptotic symmetry of MM matrix generalization of AdS3 higher spin theory. Moreover, the OPE between the charged spin-3 current and itself is determined for fixed (N, M) = (5, 4) with arbitrary k up to the third order pole. We also obtain the OPEs between charged spin-1, 2, 3 currents and neutral spin-3 current. From the last OPE, we realize that there exists the presence of the above charged quasi primary spin-4 current in the second order pole for fixed (N, M) = (5, 4). We comment on the complex free fermion realization.

The 𝒩 = 4 coset model and the higher spin algebra

By computing the operator product expansions between the first two [Formula: see text] higher spin multiplets in the unitary coset model, the (anti-)commutators of higher spin currents are obtained under the large [Formula: see text] ’t Hooft-like limit. The free field realization with complex bosons and fermions is presented. The (anti-)commutators for generic spins [Formula: see text] and [Formula: see text] with manifest [Formula: see text] symmetry at vanishing ’t Hooft-like coupling constant are completely determined. The structure constants can be written in terms of the ones in the [Formula: see text] [Formula: see text] algebra found by Bergshoeff, Pope, Romans, Sezgin and Shen previously, in addition to the spin-dependent fractional coefficients and two [Formula: see text] invariant tensors. We also describe the [Formula: see text] higher spin generators, by using the above coset construction results, for general superspin [Formula: see text] in terms of oscillators in the matrix generalization of [Formula: see text] Vasiliev higher spin theory at nonzero ’t Hooft-like coupling constant. We obtain the [Formula: see text] higher spin algebra for low spins and present how to determine the structure constants, which depend on the higher spin algebra parameter, in general, for fixed spins [Formula: see text] and [Formula: see text].

MAXIMAL SUPERGRAVITIES AND THE E10 COSET MODEL

The maximal rank hyperbolic Kac–Moody algebra 𝔢10 has been conjectured to play a prominent role in the unification of duality symmetries in string and M-theory. We review some recent developments supporting this conjecture.

POINT-SPLITTING REGULARIZATION IN N=2 SUPERCONFORMAL FIELD THEORY

In this paper, the method of point-splitting regularization is applied on the N=2 superconformal field theory, specifically the superconformal coset model formulated by Kazama and Suzuki. We obtain the correct central extensions for the N=2 superconformal algebra after many nontrivial cancellations among the various singular expressions. This shows the consistency of the point-splitting method in an N=2 superconformal system. In the process, we arrive at the Kazama–Suzuki conditions which govern the existence of an N=2 superconformal coset model in the N=1 coset model. In addition, we obtain a number of mathematical relations between the structure constants and the complex structure of the model, which allow us to simplify the U(1) current of the N=2 superconformal algebra. In the course of our analysis, we found that, at least in a two dimension conformal field theory, the operator product expansion of a composite current must be written in a way which conveys all the information of the commutator equations.

SO(3)×U(1) Isometric Instantons with Non-Abelian Hair in Four-Dimensional String Theory

We compute the exact effective string vacuum backgrounds of the level k=81/19 SU(2,1)/U(1) coset model. A compact SU(2) isometry present in this seven-dimensional solution allows one to interpret it after compactification as a four-dimensional non-Abelian SU(2) charged instanton with a singular submanifold and an SO(3) × U(1) isometry. The semiclassical backgrounds, solutions of the type II strings, present similar characteristics

Factored Coset Approach to Bosonization in the Context of Topological Backgrounds and Massive Fermions

We consider a recently proposed approach to bosonization in which the original fermionic partition function is expressed as a product of a G/G-coset model and a bosonic piece that contains the dynamics. In particular we show how the method works when topological backgrounds are taken into account. We also discuss the application of this technique to the case of massive fermions.