Comments on Background Independence and Gauge Redundancies

We describe the definition and the role background independence and the closely related notion of diffeomorphism invariance play in modern string theory. These important concepts are transformed by a new understanding of gauge redundancies and their implementation in non-perturbative quantum field theory and quantum gravity. This new understanding also suggests a new role for the so-called background-independent approaches to directly quantize the gravitational field. This article is intended for a general audience, and is based on a plenary talk given in the Loops 2007 conference in Morelia, Mexico.Comment: 8 pages, 1 figure, to appear in Adv. Sci. Let

Hypermultiplet Moduli Space and Three Dimensional Gauge Theories

We establish a relation, conjectured recently by E. Witten, between the hypermultiplet moduli space in compactifications of the heterotic string on an A-D-E singularities, and the moduli spaces of three dimensional pure gauge theories with the corresponding A-D-E gauge groups. It is possible to add a bounded number of heterotic fivebranes sitting in the singularity, while (in leading order in $\alpha'$) keeping the heterotic string perturbative. The corresponding hypermultiplet moduli space is given by the moduli space of a three dimensional gauge theory with matter.Comment: 8 pages, LATE

Noncommutative Gauge Theory, Divergences and Closed Strings

We study the renormalization of non-commutative gauge theories with matter. As in the scalar field theory cases, there are logarithmic infrared divergences resulting from integrating out high momentum modes. In order to reproduce the correct infrared behaviour, the Wilsonian effective action has to include certain ''closed string`` modes with prescribed couplings. In the case of quiver gauge theories, realized in string theory on orbifolds, we identify the required modes with a set of twisted sector fields. These closed string modes have exactly the prescribed couplings to correct the Wilsonian effective action. This provides a concrete origin for the appearance of closed string modes in noncommutative field theories.Comment: 20 pages, 2 figures, LATE

Near Hagedorn Dynamics of NS Fivebranes, or A New Universality Class of Coiled Strings

We analyze the thermodynamics of NS 5-branes as the temperature approaches the NS 5-branes' Hagedorn temperature, and conclude that the dynamics of ``Little String Theory'' is a new universality class of interacting strings. First we point out how to vary the temperature of the near extremal solution by taking into account $g_s$ corrections. The Hagedorn temperature is shown to be a limiting temperature for the theory. We then compare the thermodynamics to that of a toy model made of free strings and find basic discrepancies. This suggests a need for a new class of string interactions. We suggest that this new universality class is characterized by a strong attractive self-intersection interaction, which causes strings to be coiled. This model might also explain why ``Little String Theories'' exist in at most 5+1 dimensions.Comment: 37 pages, important signs in section 6.4 corrected, references adde

D-Branes in Linear Dilaton Backgrounds

We construct a Dirichlet boundary state for linear dilaton backgrounds. The state is conformally invariant and satisfies Cardy's conditions. We apply this construction to two dimensional string theory.Comment: 14 pages, Latex. Typos corrected and references adde

Fermi Liquids from D-Branes

We discuss finite density configurations on probe D-branes, in the presence of worldvolume fermions. To this end we consider a phenomenological model whose bosonic sector is governed by the DBI action, and whose charged sector is purely fermionic. In this model, we demonstrate the existence of a compact worldvolume embedding, stabilized by a Fermi surface on the D- brane. The finite density state in the boundary QFT is a Fermi-like liquid. We comment on the possibility of realizing non-Fermi liquids in this setup.Comment: Corrected typo