Quantum Fields and Strings

We discuss holography for geometries that are asymptotic to non-conformal brane backgrounds. The near-horizon limit of all non-conformal branes, including D-branes and the fundamental string but excluding five-branes, is conformal to $AdS_{p+2} imes S^{8-p}$ with a linear dilaton. They exhibit a generalized conformal structure, both on the QFT and on the gravitational side. We develop holographic renormalization for all these cases and discuss a number of applications. We compute the holographic 2-point functions of the stress energy tensor and gluon operator and show they satisfy the expected Ward identities and the constraints of generalized conformal structure. The holographic results are also manifestly compatible with the M-theory uplift, with the asymptotic solutions, counterterms, one and two point functions etc. of the IIA F1 and D4 appropriately descending from those of M2 and M5 branes, respectively.

The discovery of integrability in the large N limit of the prototypical realization of the AdS/CFT correspondence has raised the hope that the spectrum of scale dimensions in N=4 SYM (and strings in AdS_5 x S^5) might be known exactly, i.e. to all orders in the coupling constant. So far, most of the efforts focused on closed strings and periodic boundary conditions. In this talk I will discuss how these ideas are extended to open string and open boundary conditions. In particular how to obtain exact expressions for the boundary scattering matrices, discuss the integrability of the boundary conditions and how finite size effects may be taken into account.

We review basic properties of effective worldvolume theory describing the dynamics of Dirichlet branes in type II supergravity backgrounds and then show that the SL(2,R) symmetry of IIB supergravity allows for the existence of new supersymmetric 7-brane configurations called Q7-branes. The Q7-branes differ from the D7-branes, in particular, by their coupling to the dilaton, axion and to `magnetic\' gauge field duals thereof. The appearance of Q7-branes and their instanton duals may indicate the existence of a new, yet unexplored, perturbative vacuum of type IIB string theory.

In frustrated systems, competing interactions lead to complex phase diagrams and sometimes entirely new states of matter. Frustration often arises from the lattice geometry, leaving the system delicately balanced between a variety of possible orders. A number of normally weak effects can lead to a lifting of this degeneracy. For example, I will discuss how quantum fluctuations can stabilize a supersolid phase, where the system is at once both a crystal and a superfluid. Frustrated magnets are promising candidates for realizing spin liquid phases with exotic \'topological order\', and new kinds of quantum phase transitions that have no classical analog. Bio: Ashvin Vishwanath received his MSc from IIT Kanpur in 1996, and PhD from Princeton in 2001. After holding the Papparlardo fellowship at MIT, he joined UC Berkeley in 2004, where he is currently associate professor of physics. He specializes in theoretical condensed matter physics, especially magnetism, superconductivity and other correlated quantum phenomena in solids and cold atomic gases. Ashvin is the recipient of several awards, most recently a Sloan fellowship (2004), a Hellman foundation fellowship (2006), and an NSF CAREER Award (2007).

We will discuss the missing pieces in the understanding of the effective field theory description of string creation, the T-dual of the Hanany-Witten effect, both in the open and closed string picture. We explain the origin of the \'bare\' Chern-Simons term, so far added in by hand. There however remain unsettled issues concerning the need to modify the DBI action and the interpretation of this term in M-theory.

I will report on some work in progress with Dan Freed and Greg Moore. In an orientifold background, D-brane charge takes values in a certain twisted version of KR Theory. Moreover, there is a nontrivial background charge (\'tadpole\'). Up \'til now, this background charge has only been calculated rationally -- i.e., ignoring torsion. We derive a formula for it, over the integers. Only after \'inverting 2\', does the charge localize to the fixed point sets of the orientifold action, and we can give a compact formula for it. This reproduces the previously known rational results, but contains new information.

We discuss recent developments in the study of black holes and similar compact objects in string theory. The focus is on how these solutions are effected by higher-derivative terms in an effective action. The setting of this investigation is an off-shell formulation of five-dimensional supergravity, including terms of order four-derivatives whose precise form are determined by embedding this theory in M-theory. We find that certain singular solutions are fully regularized by the higher-derivative terms and that generic solutions receive calculable corrections to the entropy, or other relevant quantities such as the dual central charge. A particular solution studied corresponds to the geometry sourced by a fundamental string and may set the stage for a new and exciting example of holography.