Related papers: On the Semi-Relative Condition for Closed (TOPOLOG…
All solvable two-dimensional quantum gravity models have non-trivial BRST cohomology with vanishing ghost number. These states form a ring and all the other states in the theory fall into modules of this ring. The relations in the ring and…
This paper illustrates the relationship between boolean propositional algebra and semirings, presenting some results of partial ordering on boolean propositional algebras, and the necessary conditions to represent a boolean propositional…
We construct an iterative procedure to compute the vertex operators of the closed superstring in the covariant formalism given a solution of IIA/IIB supergravity. The manifest supersymmetry allows us to construct vertex operators for any…
The main focus of this paper is Bott-Borel-Weil (BBW) theory for basic classical Lie superalgebras. We take a purely algebraic self-contained approach to the problem. A new element in this study is twisting functors, which we use in…
In the light-cone closed string and toroidal membrane theories, we associate the global constraints with gauge symmetries. In the closed string case, we show that the physical states defined by the BRS charge satisfy the level-matching…
We define new topological theories related to sigma models whose target space is a 7 dimensional manifold of G_2 holonomy. We show how to define the topological twist and identify the BRST operator and the physical states. Correlation…
We study the $\NN=2$ string theory or the $\NN=4$ topological string on the deformed CHS background. That is, we consider the $\NN=2$ minimal model coupled to the $\NN=2$ Liouville theory. This model describes holographically the…
We propose an open/closed string duality in general backgrounds extending previous ideas about open string completeness by Ashoke Sen. Our proposal sets up a general version of holography that works in gravity as a tomographic principle. We…
This paper introduces and investigates the class of \textit{$k$-quasi $n$-power posinormal operators} in Hilbert spaces, generalizing both posinormal and $n$-power posinormal operators. We establish fundamental properties including matrix…
This paper explores the concept of approximate Birkhoff-James orthogonality in the context of operators on semi-Hilbert spaces. These spaces are generated by positive semi-definite sesquilinear forms. We delve into the fundamental…
We formulate the problem of counting 1/16 BPS states of N = 4 Yang Mills theory as the enumeration of the local cohomology of an operator acting on holomorphic fields on C^2. We study aspects of the enumeration of this cohomology at finite…
We derive a condition under which (0,2) linear sigma models possess a ``left-moving'' conformal stress tensor in $\bq$ cohomology (i.e. which leaves invariant the ``right-moving'' ground states) even away from their critical points. At the…
In this work, we uncover a collection of non invertible topological operators linked to the 0-, 2-, 4- and 6-form symmetries related to the type IIB superstring effective theory. By pinpointing the $\text{SL}(2,\mathbb{Z})$-covariant…
The BRST formalism has played a fundamental role in the construction of bosonic closed string backgrounds, ie. the stringy analogs of classical solutions to the field equations of general relativity. The concept of a string background has…
The purpose of the article is to generalize the concept of approximate Birkhoff-James orthogonality, in the semi-Hilbertian structure. Given a positive operator $ A $ on a Hilbert space $ \mathbb{H}, $ we define $ (\epsilon,A)- $approximate…
The cohomology of the BRS operator corresponding to a group of rigid symmetries is studied in a space of local field functionals subjected to a condition of gauge invariance. We propose a procedure based on a filtration operator counting…
In this paper, the concept of Birkhoff--James orthogonality of operators on a Hilbert space is generalized when a semi-inner product is considered. More precisely, for linear operators $T$ and $S$ on a complex Hilbert space $\mathcal{H}$, a…
The noncritical $4D$ $\cW_3$ string is a model of $\cW_3$ gravity coupled to two free scalar fields. In this paper we discuss its BRST quantization in direct analogy with that of the $2D$ (Virasoro) string. The physical operators form a…
Surface operators in gauge theory are analogous to Wilson and 't Hooft line operators except that they are supported on a two-dimensional surface rather than a one-dimensional curve. In a previous paper, we constructed a certain class of…
We study the coupling of the closed string to the open string in the topological B-model. These couplings can be viewed as gauge invariant observables in the open string field theory, or as deformations of the differential graded algebra…