Superstrings from Hamiltonian reduction

In any string theory there is a hidden, twisted superconformal symmetry algebra, part of which is made up by the BRST current and the anti-ghost. We investigate how this algebra can be systematically constructed for strings with N − 2 supersymmetries, via quantum Hamiltonian reduction of the Lie superalgebras osp(N|2). The motivation is to understand how one could systematically construct generalized string theories from superalgebras. We also briefly discuss the BRST algebra of the topological string, which is a doubly twisted N = 4 superconformal algebra.     

BRST invariant mixed string vertex for the bosonic string

We construct a BRST invariant (N + M)-string vertex including both open and closed string states. When we saturate it with N open string and M closed string physical states it reproduces their corresponding scattering amplitude. As a particular case we obtain a BRST invariant vertex for the open-closed string transition.     

A heterotic N=2 string with space–time supersymmetry

We reconsider the issue of embedding space–time fermions into the four-dimensional N=2 worldsheet supersymmetric string. A new heterotic theory is constructed, taking the right-movers from the N=4 topological extension of the conventional N=2 string but a c=0 conformal field theory supporting target-space supersymmetry for the left-moving sector. The global bosonic symmetry of the full formalism proves to be U(1,1), just as in the usual N=2 string. Quantization reveals a spectrum of only two physical states, one boson and one fermion, which fall in a multiplet of (1,0) supersymmetry.     

Numerical analysis of the twisted Eguchi-Kawai model in four dimensions

We perform a high statistics Monte Carlo calculation of the string tension in the twisted SU(N) Eguchi-Kawai model for N=36 and N=64. The string tension, calculated from Wilson loops not larger than 3 × 3, clearly shows the renormalization group scaling behaviour.     

Kähler spinning particles

We construct the U(N) spinning particle theories, which describe particles moving on Kähler spaces. These particles have the same relation to the N = 2 string as usual spinning particles have to the NSR string. We find the restrictions on the target space of the theories coming from supersymmetry and from global anomalies. Finally, we show that the partition functions of the theories agree with what is expected from their spectra, unlike that of the N = 2 string in which there is an anomalous dependence on the proper time.     

Auxiliary supergravity fields,Chern-Simons terms and the heterotic string

The generating functional of target space S-matrix amplitudes is generalized to include auxiliary field and fermionic vertex operators. Using this formalism, a new Green-Schwarz mechanism associated with the auxiliary vector field of the four-dimensional, N=1 supergravity multiplet of the heterotic string is derived.     

Quantum vortex strings: A review

The quantum worldsheet dynamics of vortex strings contains information about the 4d non-Abelian gauge theory in which the string lives. Here I tell this story. The string worldsheet theory is typically some variant of the CP^N-1 sigma-model, describing the orientation of the string in a U(N) gauge group. Qualitative parallels between 2d sigma-models and 4d non-Abelian gauge theories have been known since the 1970s. The vortex string provides a quantitative link between the two. In 4d theories with N=2 supersymmetry, the exact BPS spectrum of the worldsheet coincides with the bulk spectrum in 4d. Moreover, by tuning parameters, the CP^N-1 sigma-model can be coaxed to flow to an interacting conformal fixed point which is related to the 4d Argyres-Douglas fixed point. For theories with N=1 supersymmetry, the worldsheet theory suffers dynamical supersymmetry breaking and, more interestingly, supersymmetry restoration, in a way which captures the physics of Seiberg’s quantum deformed moduli space.     

Cavitation in holographic sQGP

We study the possibility of cavitation in the non-conformal N=^2?SU(N) theory which is a mass deformation of N=4SU(N) Yang-Mills theory. The second order transport coefficients are known from the numerical work using AdS/CFT by Buchel and collaborators. Using these and the approach of Rajagopal and Tripuraneni, we investigate the flow equations in a (1+1)-dimensional boost invariant set up. We find that the string theory model does not exhibit cavitation before phase transition is reached. We give a semi-analytic explanation of this finding.     

Nonlinear supersymmetry without the GSO projection and unstable D9-brane

Orientable open string theories containing both bosons and fermions without the GSO projection are expected to have the 10-dimensional N=2 space–time supersymmetry in a spontaneously broken phase. We study the low-energy theorem for the nonlinearly realized N=2 supersymmetry using the effective action for an unstable D9-brane. It is explicitly confirmed that the 4-fermion open string amplitudes without the GSO projection obey the low-energy theorem derived from the nonlinear N=2 supersymmetry. An intimate connection between the existence of the hidden supersymmetry and the open–open string (s–t) duality is pointed out.     

Counting dyons in N = 4 string theory

We present a microscopic index formula for the degeneracy of dyons in four-dimensional N = 4 string theory. This counting formula is manifestly symmetric under the duality group, and its asymptotic growth reproduces the macroscopic Bekenstein-Hawking entropy. We give a derivation of this result in terms of the type 11 five-brane compactified on K3, by assuming that its fluctuations are described by a closed string theory on its world-volume. We find that the degeneracies are given in terms of the denominator of a generalized super Kac-Moody algebra. We also discuss the correspondence of this result with the counting of D-brane states.     

Heterotic string compactification on N = 2 superconformal theories with c = 9

We study (2, 2) compactifications of the heterotic string by tensoring the discrete N = 2 superconformal series. We construct all models with c = 9 that preserve N = 1 spacetime supersymmetry and discuss some of their properties.     

Instanton strings and hyper-Kähler geometry

We discuss two-dimensional sigma models on moduli spaces of instantons on K3 surfaces. These N = (4, 4) superconformal field theories describe the near-horizon dynamics of the D1-D5-brane system and are dual to string theory on AdS³. We derive a precise map relating the moduli of the K3 type 1113 string compactification to the moduli of these conformal field theories and the corresponding classical hyper-Kahler geometry. We conclude that in the absence of background gauge fields, the metric on the instanton moduli spaces degenerates exactly to the orbifold symmetric product of K3. Turning on a self-dual NS B-field deforms this symmetric product to a manifold that is diffeomorphic to the Hilbert scheme. We also comment on the mathematical applications of string duality to the global issues of deformations of hyper-Kähler manifolds.     

HCIZ integral and 2D Toda lattice hierarchy

The expression of the large N Harish Chandra–Itzykson–Zuber (HCIZ) integral in terms of the moments of the two matrices is investigated using an auxiliary unitary two-matrix model, the associated biorthogonal polynomials and integrable hierarchy. We find that the large N HCIZ integral is governed by the dispersionless Toda lattice hierarchy and derive its string equation. We use this to obtain various exact results on its expansion in powers of the moments.     

On the spectrum of (2,2) compactification of the heterotic string on conformal field theories

We study (2, 2) compactifications of the heterotic string by tensoring the degenerate N = 2 superconformal series. We recently constructed all models with c = 9 that preserve N = 1 spacetime supersymmetry. Here we extend this analysis by investigating the spectrum of our models. The number of generations and anti-generations is calculated and we comment on the conjectured relation between these conformal field theories and Calabi-Yau compactifications.     

A string calculation of the Kähler potentials for moduli of ZN orbifolds

We present a method for calculating the Kähler potentials of the moduli of Z_N orbifolds directly from string theory. The explicit Kähler potentials associated with b_(1,1) and b_(1,2) moduli are given for any (2,0) symmetric Z_N orbifold. These results are exact at the string tree level.     

A scaling limit with many noncommutativity parameters

We derive the worldsheet propagator for an open string with different magnetic fields at the two ends, and use it to compute two distinct noncommutativity parameters, one at each end of the string. The usual scaling limit that leads to noncommutative Yang–Mills can be generalized to a scaling limit in which both noncommutativity parameters enter. This corresponds to expanding a theory with U(N) Chan–Paton factors around a background U(1)^N gauge field with different magnetic fields in each U(1).     

Stochastic finite element analysis of a vibrating string

The response of a vibrating string subjected to spatial white noise excitation is analyzed by using the finite element (Galerkin) method. The discretization is achieved by using basis functions in the spatial and random spaces. The continuous time finite element equations are then integrated in time by using the central difference algorithm. It is shown that when the string is divided into N segments, the Galerkin approach leads to N(N?1) degrees of freedom which are governed by N subsets of equations. The subsets are similar in form. Furthermore, for a uniform string, they are governed by the same operator as that which governs the system of (N?1) degrees of freedom arising from the corresponding deterministic problem. Random initial conditions can also be treated by the same method, and the analysis of strings with initial conditions described by the standard Brownian process is carried out. Numerical results are given to illustrate the stochastic response.