Related papers: On the BRST Operator of $W$-Strings
We provide several perturbation theorems regarding closable operators on a real or complex Hilbert space. In particular we extend some classical results due to Hess--Kato, Kato--Rellich and W\"ust. Our approach involves ranges of matrix…
In this pedagogical mini course the basics of the derivation of the noncommutative structures appearing in string theory are reviewed. First we discuss the well established appearance of the noncommutative Moyal-Weyl star-product in the…
Recently, we proposed a novel entry of the pp-wave holographic dictionary, which equated the Berenstein-Maldacena-Nastase (BMN) two-point functions in free $\mathcal{N}=4$ super-Yang-Mills theory with the norm squares of the quantum unitary…
Quantum Lie algebras (an important class of quadratic algebras arising in the Woronowicz calculus on quantum groups) are generalizations of Lie (super) algebras. Many notions from the theory of Lie (super)algebras admit ``quantum''…
Each bounded operator T on an infinite dimensional Hilbert space H is a sum of three operators that are similar to positive operators; two such operators are sufficient if T is not a compact perturbation of a scalar. The spectra of L\"uders…
We present a compact expression for a coherent vertex operator in superstring theory, in the Neveu-Schwarz sector, that can be easily extended to the Ramond sector by supersymmetric transformations in target space. We give also an explicit…
We describe the complete cohomology of the Berkovits BRST operator for the superparticle. It is non-zero at eight ghost numbers, splitting into two quartets, the members of each quartet being completely isomorphic. Based only on…
In these talks we review some of the recent results on open strings and noncommutative gauge theories, starting from the early calculations of open strings in a constant electromagnetic background. We discuss both the neutral string and the…
A covariant map between the Ramond-Neveu-Schwarz (RNS) and pure spinor formalisms for the superstring is found which transforms the RNS and pure spinor BRST operators into each other. The key ingredient is a dynamical twisting of the ten…
In this paper, we introduce the B-discrete spectrum of an unbounded closed operator and we prove that a closed operator has a purely B-discrete spectrum if and only if it has a meromorphic resolvent. After that, we study the stability of…
We first analyze the anti-BRST and double BRST structures of a certain higher derivative theory that has been known to possess BRST symmetry associated with its higher derivative structure. We discuss the invariance of this theory under…
We show that the one loop amplitudes of open and closed string theory in a constant background two-form tensor field are characterized by an effective string tension larger than the fundamental string tension, and by the appearance of…
Light-cone gauge NSR string theory in noncritical dimensions should correspond to a string theory with a nonstandard longitudinal part. Supersymmetrizing the bosonic case [arXiv:0909.4675], we formulate a superconformal worldsheet theory…
A new set of boundary conditions for string propagators is proposed in this paper. The boundary conditions are parametrized by a complex number $\lambda$. Under these new boundary conditions, the left-moving and right-moving modes are…
In the available literature, only the Becchi-Rouet-Stora-Tyutin (BRST) symmetries are known for the Jackiw-Pi model of the three (2 + 1)-dimensional (3D) massive non-Abelian gauge theory. We derive the off-shell nilpotent (s_{(a)b}^2 = 0)…
We study various spectral theoretic aspects of non-self-adjoint operators. Specifically, we consider a class of factorable non-self-adjoint perturbations of a given unperturbed non-self-adjoint operator and provide an in-depth study of a…
We study weighted composition operators on Hilbert spaces of analytic functions on the unit ball with kernels of the form $(1-<z,w>)^{-\gamma}$ for $\gamma>0$. We find necessary and sufficient conditions for the adjoint of a weighted…
Some time ago we have introduced a route to provide confinement in the sense that particle excitations would appear from condensates of fields that do not have physical asymptotic states. We envisaged this mechanism in an asymmetric vacuum…
We construct the unintegrated vertex operator at the first mass level of the open superstring from the OPE of massless vertices. Using BRST cohomology manipulations, the tree amplitude of two massless and one massive state is rewritten in…
In this paper, the BRST symmetry transformation is presented for the noncommutative U(N) gauge theory. The nilpotency of the charge associated to this symmetry is then proved. As a consequence for the space-like non-commutativity parameter,…