Related papers: The Berkovits-Vafa Construction and Nonlinear Real…
I argue that string theory can not be a serious candidate for the Theory of Everything, not because it lacks experimental support, but because of its algebraic shallowness. I describe two classes of algebraic structures which are deeper and…
The conformal anomaly and the Virasoro algebra are fundamental aspects of 2D conformal field theory and conformally covariant models in planar random geometry. In this article, we explicitly derive the Virasoro algebra from an…
We construct the K=8 fractional superconformal algebras. There are two such extended Virasoro algebras, one of which was constructed earlier, involving a fractional spin (equivalently, conformal dimension) 6/5 current. The new algebra…
Nonlinear realizations describing the spontaneous breakown of supersymmetry and R symmetry are constructed using the Goldstino and R axion fields. The associated R current, supersymmetry current and energy-momentum tensor are shown to be…
Singularities of Spin(7) manifolds are considered in the worldsheet approach, and it is argued that the internal CFT describing a singular spin(7) has an enhanced ${\cal SW}({3\over 2},{3\over 2},2)$ algebra tensored with ${\cal N}=1$…
We consider Carrollian conformal field theories in two dimensions and construct the boundary Carrollian conformal algebra (BCCA), opening up innumerable possibilities for further studies, given the growing relevance of Carrollian…
A string field theory of (p,q) minimal superstrings is constructed with the free-fermion realization of 2-component KP (2cKP) hierarchy, starting from 2-cut ansatz of two-matrix models. Differential operators of 2cKP hierarchy are…
Lian and Zuckerman proved that the homology of a topological chiral algebra can be equipped with the structure of a BV-algebra; \ie one can introduce a multiplication, an odd bracket, and an odd operator $\Delta$ having the same properties…
We revisit the non-linear sigma model approach to string theory with the closed superstring field theory. We construct the string field theory around the non-linear sigma model background with the patch-by-patch description. We show that…
We use an argument of Romans showing that every Virasoro construction leads to realizations of $W_3$, to construct $W_3$ realizations on arbitrary affine Lie algebras. Solutions are presented for generic values of the level as well as for…
Spacetime Virasoro and affine Lie algebras for strings propagating in AdS3 are known to all orders in $\alpha'$. The central extension of such algebras is a string vertex, whose expectation value can depend on the number of long strings…
This thesis presents several new insights on the interface between mathematics and theoretical physics, with a central role for fermions on Riemann surfaces. First of all, the duality between Vafa-Witten theory and WZW models is embedded…
Given a simple, simply laced, complex Lie algebra $\bfg$ corresponding to the Lie group $G$, let $\bfnp$ be the subalgebra generated by the positive roots. In this paper we construct a BV-algebra $\fA[\bfg]$ whose underlying graded…
We show that the Zamolodchikov's and Polyakov-Bershadsky nonlinear algebras $W_3$ and $W_3^{(2)}$ can be embedded as subalgebras into some {\em linear} algebras with finite set of currents. Using these linear algebras we find new field…
The main limitations of string field theory arise because its present formulation requires a background representing a classical solution, a background defined by a strictly conformally invariant theory. Here we sketch a construction for a…
We construct analytic solutions of open superstring field theory in the Berkovits formulation using boundary condition changing operators under some regularity conditions, extending the previous construction in the bosonic string. We also…
We study some features of infinite resolutions of Koszul algebras motivated by the developments in the string theory initiated by Berkovits.
The (bosonic) Virasoro minimal string, which relates worldsheet string theory to a deformation of the JT gravity matrix model, provides an interesting example of a tractable matrix/string duality. We explore its $\mathcal{N} =1$…
In this paper, we investigate the spinor field realizations of the $W_{2,4}$ algebra, making use of the fact that the $W_{2,4}$ algebra can be linearized through the addition of a spin-1 current. And then the nilpotent BRST charges of the…
A nonlinear realization of super $W_{\infty}$ algebra is shown to exist through a consistent superLax formulation of super KP hierarchy. The reduction of the superLax operator gives rise to the Lax operators for $N=2$ generalized super KdV…