Dennis Nemeschansky

Supersymmetric Randall-Sundrum scenario

We present the supersymmetric version of the minimal Randall-Sundrum model with two opposite tension branes.

Superconformal fixed points with En global symmetry

Abstract We obtain the elliptic curve and the Seiberg-Witten differential for an N = 2 superconformal field theory which has an ES global symmetry at the strong coupling point π = e πi /3 . The differential has 120 poles corresponding to half the charged states in the fundamental representation of E 8 , with the other half living on the other sheet. Using this theory, we flow down to E 7 , E 6 and D 4 . A new feature is a λ SW for these theories based on their adjoint representations. We argue that these theories have different physics than those with λ SW built from the fundamental representations.

String propagation in backgrounds with curved space-time☆

Abstract We study propagation of bosonic strings and superstrings in background metrics with curved space-time using non-compact current algebras. We discuss 2 + 1 dimensional (super)strings on the SO(2,1) group manifold. Using a coset model we construct a ( d − 1)+1 dimensional de Sitter (super)strings for d =2,3,4…10 or 26. We also discuss the posibility of a discrepancy in counting the number of time (i.e. non-compact) coordinates for the classical string versus the quantum string. We illustrate this with several examples. We show evidence that a string or superstring propagating in a background with curved time cannot be excited to arbitrarily high states and that it is unitary only in low lying states. We offer a possible interpretation of this phenomenon.

Feigin-Fuchs representation of su(2)k Kac˘-Moody algebra

Abstract We construct the Feigin-Fuchs representation for the su (2)k Kac-Moody algebra in terms of three bosons compactified on a lorentzian lattice with signature (-, +, +). We arrive at this result by first solving the same problem for Zk parafermions.

Beta functions and S-matrix in string theory

Abstract The relationship between sigma model β-functions and string theory scattering amplitudes is proved. We derive our results for the closed bosonic string using the weak field expansion around the flat space. The equations of motion for all the background fields, including the heavy fields are considered. We show that the effective equations for the light fields are obtained by integrating out the heavy fields. It is shown that the contributions to the β-functions come from the boundary of moduli space on a punctured Riemann surface. String loop corrections to the equations of motion are also studied.

A BRST PRIMER

We develop a Hamiltonian formulation of the BRST method for quantizing constrained systems. The rigid rotor is studied in detail and the similarity of this simple quantum system to a gauge theory is explicitly demonstrated. The system is quantized as a gauge theory and then the similarity between BRST and the Gupta-Bleuler approach is displayed. We also apply our formalism to true gauge theories. Both Abelian and non-Abelian gauge theories are studied in detail. Finally, the Hamiltonian treatment of the relativistic and the spinning relativistic particle is presented.

Bosons, fermions and Thirring strings

Abstract All toroidal compactifications of string theories are described in terms of two-dimensional fermions. The compactification parameters (the metric, the antisymmetric tensor and the gauge field) are incorporated into four-Fermi Thirring-like interactions on the world sheet. An alternative formulation removes the Thirring interactions and considers free fermions with twisted boundary conditions. In this description, there are several twisted sectors, and a generalized GSO projection is necessary for modular invariance.

Multi-loop twist field correlation functions for ZN orbifolds

Abstract We calculate the correlation functions of bosonic twist fields for Z N orbifolds on Riemann surfaces of arbitrary genus.

Supersymmetric radion in the Randall-Sundrum scenario

We derive the effective action for the radion supermultiplet in the supersymmetric Randall-Sundrum model with two opposite tension branes.

N = 2 SUPER YANG-MILLS AND SUBGROUPS OF SL(2,Z)

We discuss SL(2,Z) subgroups appropriate for the study of N = 2 super Yang-Mills with Nf = 2n flavors. Hyperelliptic curves describing such theories should have coefficients that are modular forms of these subgroups. In particular, uniqueness arguments are sufficient to construct the SU(3) curve, up to two numerical constants, which can be fixed by making some assumptions about strong coupling behavior. We also discuss the situation for higher groups. We also include a derivation of the closed form β-function for the SU(2) and SU(3) theories without matter, and the massless theories with Nf = n.