Quantum Strings and Superstrings

We give an introduction to a new approach to the covariant quantization of superstrings. After a brief review of the classical Green--Schwarz superstring and Berkovits' approach to its quantization based on pure spinors, we discuss our covariant formulation without pure spinor constraints. We discuss the relation between the concept of grading, which we introduced to define vertex operators, and homological perturbation theory, and we compare our work with recent work by othe...

We show how starting with one-string space of states in BRST formalism one can construct a large class of physical quantities containing, in particular, scattering amplitudes for bosonic string and superstring. The same techniques work for heterotic string.

Physical states of the superstring can be described in light-cone gauge by acting with transverse bosonic $\alpha_{-n}^{j}$ and fermionic $\bar{q}_{-n}^{\dot{a}}$ operators on an $SO\left(8\right)$-covariant superfield where $j,\dot{a}=1$ to $8$. In the pure spinor formalism, these states are described in an $SO\left(9,1\right)$-covariant manner by the cohomology of the BRST charge $Q=\frac{1}{2\pi i}\oint\lambda^{\alpha}d_{\alpha}$. In this paper, a similarity transformation...

Introductory Notes in Bosonic String Theory and its Canonical Quantization.

We briefly review superstring theories, highlighting the important concepts, developments, and open problems of the subject.

We present the covariant BRST quantization of the super-D-string. The non-vanishing supersymmetric U(1) field strength ${\cal F}$ is essential for the covariant quantization of the super-D-string as well as for its static picture. A SO(2) parameter parametrizes a family of local supersymmetric (kappa symmetric) systems including the super-D-string with ${\cal F}\ne 0$ and the Green-Schwarz superstring with ${\cal F}= 0$. We suggest that $E^1$ (canonical conjugate of U(1) gaug...

I review the construction of an action for open superstring field theory which does not suffer from the contact term problems of other approaches. I also discuss a possible generalization of this action for closed superstring field theory.

In these lecture notes, an introduction to superstring theory is presented. Classical strings, covariant and light-cone quantization, supersymmetric strings, anomaly cancelation, compactification, T-duality, supersymmetry breaking, and threshold corrections to low-energy couplings are discussed. A brief introduction to non-perturbative duality symmetries is also included.

After reviewing the Green-Schwarz superstring using the approach of Siegel, the superstring is covariantly quantized by constructing a BRST operator from the fermionic constraints and a bosonic pure spinor ghost variable. Physical massless vertex operators are constructed and, for the first time, N-point tree amplitudes are computed in a manifestly ten-dimensional super-Poincar\'e covariant manner. Quantization can be generalized to curved supergravity backgrounds and the ver...

At the present time, string theory (and its generalizations) remain relatively abstruse subjects to the particle phenomenologist and experimentalist. Yet, striking developments of the last two years offer hope that a fundamental non-perturbative formulation of this theory will be found, and that this formulation will permit us to make contact with supersymmetric standard-model physics. This article is based on a talk which attempted to convey the essence of these recent devel...