GRAVITY THEORY SEMINARS 2005
``What is time?''
Time is the quantitative characterization of correlations between physical processes and points traversed on a standard trajectory called a clock. The scale factor of the universe is such a clock.
``String/gauge-theory duality and ferromagnetic spin chains''
It has long been suspected that strings play
a role in understanding the low energy limit of non-abelian gauge
theories and in particular in describing hadrons as bound states of
quarks and gluons. This idea has recently been made precise by the
AdS/CFT correspondence which provides a concrete example of the
relation between gauge and string theories.
After reviewing these ideas I am going to concentrate in two aspects of the correspondence: First, in the way in which, for certain theories, quarks can be incorporated and their bound states can be computed. Second, in a procedure that allows to derive an effective action for a string directly from the field theory. Here, the ferromagnetic (spin 1/2) Heisenberg chain plays a central role: on one hand it arises naturally in the field theory and on the other, it can be seen that its low energy excitations (spin waves) can be interpreted as strings. It therefore provides a bridge between both descriptions.
``Adventures in String Theory: From Black Holes to QCD''
String theory was originally invented to explain quark confinement and the spectrum of hadrons in QCD, although we now understand it as a theory of quantum gravity. However, recent developments show that quantum gravity in certain curved spacetimes is actually equivalent to a strongly-coupled gauge theory. I will introduce this equivalence with three simple examples: I will show how to see quantum string theory emerging from gauge theory, explain the relation between the deconfinement phase transition and black hole formation, and discuss string theory implications for gluon scattering amplitudes.
``QCD amplitudes and string theory''
The number of Feynman diagrams which contribute to an n-particle scattering amplitude in quantum chromodynamics grows faster than factorially with the number n, making it difficult to compute the amplitudes explicitly. The construction of more efficient computational methods which also expose otherwise hidden rich mathematical structure has benefited substantially from string theory input. In addition, string theory dualities offer a promising strategy for solving strongly-coupled gauge theories such as QCD. I will review the most recent progress in these directions.
``Finite Temperature Field Theory and Black Holes''
In this talk I will use the AdS/CFT correspondence to study some of the most interesting puzzles of black holes. The singularity and the region near it can be probed by examining the analytic structure of certain finite-temperature gauge theory correlation functions. This structure turns out to be quite subtle, and contains some interesting surprises. The long-time behavior of the same correlators reveals a puzzle which constitutes a very precise formulation of the black hole information paradox. I will discuss a possible resolution of this problem involving a quantum sum over bulk geometries.
``The Problem of Motion in General Relativity as a Theory of Scales''
In this talk I will discuss an approach to solving the problem of motion using effective field theory techniques. In particular I will discuss the calculation of the motion of a binary system in the point particle appoximation and show how finite size effects can be incorporated using higher dimensional world line operators. Classical divergencs due to the point particle limit will be treated using standard remormalization techniques and lead to non-trivial renormalization group flows.
``Exact solitary wave solutions for discrete λ φ4 field theory in 1+1 dimensions''
We have found exact, periodic, time-dependent solitary wave solutions of a discrete φ4 field theory model. For finite lattices, depending on whether one is considering a repulsive or attractive case, the solutions are either Jacobi elliptic functions sn(x,m) (which reduce to the kink function tanh(x) for m → 1), or they are dn(x,m) and cn(x,m) (which reduce to the pulse function sech(x) for m → 1). We have studied the stability of these solutions numerically, and we find that our solutions are linearly stable in most cases. We show that this model is a Hamiltonian system, and that the effective Peierls-Nabarro barrier due to discreteness is zero not only for the two localized modes but even for all three periodic solutions. We also present results of numerical simulations of scattering of kink--anti-kink and pulse--anti-pulse solitary wave solutions.
``Generalizing General Covariance''
We have no firm idea of what modifications of general relativity will be required to develop a theory of "quantum gravity." How can the principle of general covariance be generalized so that it provides a criterion for any such modification, such as Sorkin's causal set theory, that abandons differentiable manifolds as its basis? Once we realize that diffeomorphisms are just a type of permutation of the elements of the manifold, and that diffeomorphism invariance is just the requirement that the elements of the manifold have no inherent spatio-temporal properties, it becomes clear how to generalize diffeomorphism invariance, and the principle of general permutation invariance is proposed as the correct generalization.
``What's Wrong with Noncommutative Spacetime''
The idea of noncommutative spacetime has been motivated by uncertainty relations, from String Theory, to explain the Standard Model, or simply as an interesting possibility. However, the moduli space of "slightly" noncommutative spaces is quite different from that of (commutative) Riemannian manifolds; there are geometric obstructions to deforming a Riemannian manifold into noncommutative geometry. This implies that physical spacetime is not 4 dimensional and slightly noncommutative. More optimistically, it suggests that noncommutativity could be a mechanism for suppressing spurious extra dimensions in physical theories.
``Gravity as an Effective Field Theory: Short Distance and Initial State Effects in Inflation''
Classical general relativity is best understood as a low energy effective field theory. However, unlike other effective theories with a fixed short distance cutoff, a fixed short distance cutoff in dynamical spacetimes can lead to violations of energy conservation on macroscopic scales. Requiring that there be no such violations imposes model independent constraints on allowed short distance and initial state effects in inflation. The effective action for gravity is determined by the same requirement, and the Equivalence Principle allows for an essentially unique modification of general relativity at macroscopic distances due to quantum effects.
``Quantum Theory as an Emergent Phenomenon''
I give a brief overview of my book with this title, which proposes that quantum theory is not a complete, final theory, but is in fact an emergent phenomenon arising from a deeper level of dynamics. The dynamics at this deeper level is taken to be an extension of classical dynamics to non-commuting matrix variables, with cyclic permutation inside a trace used as the basic calculational tool. With plausible assumptions, quantum theory is shown to emerge as the statistical thermodynamics of this underlying theory, with the canonical commutation-anticommutation relations derived from a generalized equipartition theorem. Brownian motion corrections to this thermodynamics are argued to lead to state vector reduction and to the probabilistic interpretation of quantum theory, making contact with recent phenomenological proposals for stochastic modifications to Schrodinger dynamics.
``Black hole microstates and counting regular supergravity solutions''
We discuss general methods to quantize moduli spaces of regular horizonless (super)gravity solutions. This has applications to black hole microstate counting "without D-branes" in Mathur's picture of stringy black holes, as well as to the quantum-mechanical description of the 1/2 BPS sector of AdS/CFT.
``Spin-orbit resonance in black hole binaries''
We analyze the post-Newtonian equations of motion for binary black holes, including spin-orbit and spin-spin precession terms. For a subset of spin orientations, the binary system can get locked in to a resonance configuration where the individual spins precess at the same frequency. By including radiation reaction, we show that systems initially far from resonance can get captured into a locked configuration. This results in a net evolution of the distribution in spin space, with possible implications for LIGO detection and parameter estimation.
``Analog quantum gravity phenomenology in a 2-BEC system''
Effective field theories (EFTs) have been widely used as a framework in order to place constraints on the Planck suppressed Lorentz violations predicted by various models of quantum gravity. There are however technical problems in the EFT framework when it comes to ensuring that small Lorentz violations remain small -- this is the essence of the "naturalness" problem. We present an extended "emergent" space-time based on the "analogue gravity" programme by investigating a specific condensed-matter system that is in principle capable of simulating both a massless and a massive Klein-Gordon equation in curved spacetime. Specifically, we consider the class of two-component BECs subject to laser-induced transitions between the components, and we show that this model is an example for Lorentz invariance violation due to ultraviolet physics. Furthermore our model explicitly avoids the "naturalness problem", and makes specific suggestions regarding how to construct a physically reasonable quantum gravity phenomenology.
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