Related papers: SL(2, $\mathbb C$) quartic vertex for closed strin…

We formulate the general construction for singular vectors in Verma modules of the affine sl(2|1) superalgebra. We then construct sl(2|1) representations out of the fields of the non-critical N=2 string. This allows us to extend naturally…

In this paper we introduce the bosonic generators of the $sp(4,R)$ algebra and study some of their properties, based on the $SU(1,1)$ and $SU(2)$ group theory. With the developed theory of the $Sp(4,R)$ group, we solve the interaction part…

Generalizing local Gromov-Witten theory, in this paper we define a local version of symplectic field theory. When the symplectic manifold with cylindrical ends is four-dimensional and the underlying simple curve is regular by automatic…

The geometry of 4-string contact interaction of closed string field theory is characterized using machine learning. We obtain Strebel quadratic differentials on 4-punctured spheres as a neural network by performing unsupervised learning…

We extend our previous study of quaternionic analysis based on representation theory to the case of split quaternions H_R. The special role of the unit sphere in the classical quaternions H identified with the group SU(2) is now played by…

We study the matter part of the algebra of open string fields using the 3-string vertex over the sliver state, which we call ``comma vertex''. By generalizing this comma vertex to the $N$-string overlap, we obtain a closed form of the…

We construct and classify all space-like minimal surfaces in AdS_3 x S^3 which globally admit coordinates with constant induced metric on both factors. Up to O(2,2) x O(4) transformations all these surfaces, except one class, are…

In six spacetime dimensions, the heterotic string is dual to a Type $IIA$ string. On further toroidal compactification to four spacetime dimensions, the heterotic string acquires an $SL(2,\BbbZ)_S$ strong/weak coupling duality and an…

We extend the recently constructed double field theory formulation of the low-energy theory of the closed bosonic string to the heterotic string. The action can be written in terms of a generalized metric that is a covariant tensor under…

The target space theory of the N=(2,1) heterotic string may be interpreted as a theory of gravity coupled to matter in either $1+1$ or $2+1$ dimensions. Among the target space theories in $1+1$ dimensions are the bosonic, type II, and…

The operator formalism of the first quantized string theory is applied to the stringy excitations in the linear dilaton background. In particular, the normal-ordered vertex operators in the old-covariant spectrum of the bosonic open string,…

We show how bosonic (free field) representations for so-called degenerate conformal theories are built by singular vectors in Verma modules. Based on this construction, general expressions of conformal blocks are proposed. As an example we…

We present a new representation of the string vertices of the cubic open string field theory. By using this three-string vertex, we attempt to identify open string fields as huge-sized matrices by following Witten's idea. By using these…

We consider the Feigin-Fuchs-Felder formalism of the $SU(2)_k\times SU(2)_l/SU(2)_{k+l}$ coset minimal conformal field theory and extend it to higher genus. We investigate a double BRST complex with respect to two compatible BRST charges,…

Using a new type of simulation algorithm for the standard SU(3) lattice gauge theory that yields results with unprecedented precision, we confirm the presence of a $\gamma/r$ correction to the static quark potential at large distances $r$,…

Remarkably simple closed-form expressions for the elements of the groups SU(n), SL(n,R), and SL(n,C) with n=2, 3, and 4 are obtained using linear functions of biquaternions instead of n x n matrices. These representations do not directly…

We construct and study SUSY lattice vertex algebras. As a simple example, we obtain the simple vertex algebra associated to the vertex algebra $V_c(N3)$ of central charge $c=3/2$, as the SUSY lattice vertex algebra associated to…

The construction of gauge invariant states of SU(3) lattice gauge theories has garnered new interest in recent years, but implementing them is complicated by the need for SU(3) Clebsch-Gordon coefficients. In the loop-string-hadron (LSH)…

We study the topological B-model on a deformed $\Z_2$ orbifolded conifold by investigating variation of complex structures via quantum Kodaira-Spencer theories. The fermionic/brane formulation together with systematic utilization of…

It has long been known that in principle, the genus g vacuum amplitude for bosonic strings or superstrings in 26 or 10 dimensions can be entirely determined from conditions of holomorphy. Moreover, this has been done in practice for bosonic…