Scientific Series

Higher derivative extensions of the Standard Model are renormalizable but without a quadratic divergent higgs mass. Electroweak presision data constraint the scale of the higher derivatives to at least a few TeV, but then these models have no flavor problem. We skim through these and other interesting results, most remarkably causality as an emergent characteristic at long distances. But we start by explaining the indefinite metric quantization procedure proposed by Lee and Wick which is necessary for unitary.

More than forty years ago Nobel laureate P.W. Anderson studied the overlap between two nearby ground states. The result that the overlap tends to zero in the thermodynamics limit was catastrophic for those times. More recently the study of the overlap between ground states, i.e. the fidelity, led to the formulation of the so called fidelity approach to (quantum) phase transition (QPT). This new approach to QPT does not rely on the identification of order parameters or symmetry pattern; rathers it embodies the theory of phase transitions with an operational meaning in terms of measurements. Nowadays orthogonality of ground states is much less surprising. I will provide the general scaling behavior of the fidelity at regular and at critical points of the phase diagrams, Anderson's result being a particular case. These results are useful to many areas of theoretical physics. A related quantity extensively studied here, the fidelity susceptibility, is well known in various other contexts under different names. In metrology it is called quantum Fisher information; in the theory of adiabatic computation it represents the figure of merit for efficient computation; in yet another context it is known as (real part of) the Berry geometric tensor.

Theories with extra dimensions naturally give rise to a large landscape of vacua stabilized by flux. I will show that the fastest decay is a giant leap to a wildly distant minimum, in which many different fluxes discharge at once. Indeed, the fastest decay is frequently the giantest leap of all, where all the fluxes discharge at once, which destabilizes the extra dimensions and begets a bubble of nothing. Finally, I will discuss how these giant leaps are mediated by the nucleation of "monkey branes" that wrap the extra dimensions.

We will discuss two topics. First we will revisit the asymptotic structure of classical de Sitter space. In particular we will construct charges at future infinity (I^+) and obtain the asymptotic symmetry group drawing parallels with the BMS group of flat space. Secondly, move away from the region I^+ and study the space living near the cosmological horizon by considering large rotating Nariai black holes whose size tends to that of the cosmological horizon. We will examine the resulting near (cosmological) horizon geometry and find an interesting asymptotic structure containing the Virasoro algebra, suggestive of a holographic interpretation.

A picture can be used to represent an experiment. In this talk we will consider such pictures and show how to turn them into pictures representing calculations (in the style of Penrose's diagrammatic tensor notation). In particular, we will consider circuits described probabilistically. A circuit represents an experiment where we act on various systems with boxes, these boxes being connected by the passage of systems between them. We will make two assumptions concerning such circuits. These two assumptions allow us to set up the duotensor framework (a duotensor is like a tensor except that each position is associated with two possible bases). We will see that quantum theory can be formulated in this framework. Each of the usual objects of quantum theory (states, measurements, transformations) are special cases of duotensors. The framework is motivated by the objective of providing a formulation of quantum theory which is local in the sense that, in doing a calculation pertaining to a particular region of spacetime, we need only use mathematical objects that pertain to this same region. This is, I argue, a prerequisite in a theory of quantum gravity. Reference for this talk: http://arxiv.org/abs/1005.5164

The Z2 orbifold of N=4 SYM can be connected to N=2 superconformal QCD by a marginal deformation. The spin chains in this marginal family of theories have sufficient symmetry that allows for an all-loop determination of dispersion relation of BMN magnons. The exact two body S matrix is also fixed up to an overall phase. The exact dispersion relation of the magnon can be obtained from the matrix model of lowest modes on S^3, as well. I'll also talk briefly about some progress made towards the string dual of N=2 superconformal QCD, the endpoint of the deformation.

Topological order is a new kind of collective order which appears in two-dimensional quantum systems such as the fractional quantum Hall effect and brings about rather unusual particles: unlike bosons or fermions these anyons obey exotic statistics and can be exploited to perform quantum computation. Topological order also implies that quantum states at low energies exhibit a very subtle, yet intricate inner structure. Remarkably, both phenomena can be studied in relatively simple spin systems (like Kitaev's quantum double models and the ubiquitous toric code) which in fact capture the essential properties of entire topological phases of matter in many important cases. What is the relationship between these topological phases? Reviewing recent work I will explain how they arrange themselves in a landscape of dualities and hierarchies. In particular, I will focus on two aspects: first, a duality between electric and magnetic quasiparticles in generalized quantum double models and second, a hierarchy construction of quantum states which are related by the condensation of topological charges.

There has been a growing interest in electromagnetic counterparts to gravitational wave signals. Of particular interest here, are counterparts to gravitational wave signals from super-massive black hole mergers. We consider a circumbinary disk, hollowed out by torques from the binary, and provide an analytic solution to its response following merger. There are two changes to the potential which occur during the merger process: an axisymmetric mass-energy loss and asymmetric recoil kick given to the resulting super-massive black hole. With a brief literature search we argue that, for fiducial disk values and for black hole spins aligned and anti-aligned with the orbital angular momentum, throughout the majority of parameter space the mass loss well dominates the effects of the recoil kicks on the circumbinary disk. This, along with assuming vertical hydrodynamic equilibrium, reduces the problem to one dimension. Using a 1D hydrodynamical code we explore the majority of parameter space and describe the different possible flows. In the 1D case, we give analytic approximations for the locations of the first shocks, their strengths, and the final density after the disk has again reached a steady state. This allows one to determine the temperature jump across the shock front and determine the observability, modulo the yet unknown disk mass.

The functional Renormalization Group is a continuum method to study quantum field theories in the non-perturbative regime. In Yang-Mills theory, it can be used to relate fully nonperturbative low-order correlation functions in particular gauges to observables such as confinement order parameters. As a special application, we determine the order of the phase transition and the critical temperature for various gauge groups (SU(N), N=3,.,12, Sp(2) and E(7)). This also allows to investigate what determines the order of the deconfinement phase transition. Furthermore we study the non-perturbative effective potential for the field strength, where we observe the formation of a gluon condensate in the vacuum.

Quantum error correcting codes and topological quantum order (TQO) are inter-connected fields that study non-local correlations in highly entangled many-body quantum states. In this talk I will argue that each of these fields offers valuable techniques for solving problems posed in the other one. First, we will discuss the zero-temperature stability of TQO and derive simple conditions that guarantee stability of the spectral gap and the ground state degeneracy under generic local perturbations. These conditions thus can be regarded as a rigorous definition of TQO. Our results apply to any quantum spin Hamiltonian that can be written as a sum of geometrically local commuting projectors on a D-dimensional lattice. This large class of Hamiltonians includes Levin-Wen string-net models and Kitaev's quantum double models. Secondly, we derive upper bounds on the parameters of quantum codes with local check operators and discuss the implications for feasibility of a quantum self-correcting memory.

I will review some recent advances on the line of deriving quantum field theory from pure quantum information processing. The general idea is that there is only Quantum Theory (without quantization rules), and the whole Physics---including space-time and relativity---is emergent from the processing. And, since Quantum Theory itself is made with purely informational principles, the whole Physics must be reformulated in information-theoretical terms. Here's the TOC of the talk: a) Very short review of the informational axiomatization of Quantum Theory; b) How space-time and relativistic covariance emerge from the quantum computation; c) Special relativity without space: other ideas; d) Dirac equation derived as information flow (without the need of Lorentz covariance); e) Information-theoretical meaning of inertial mass and Planck constant; f) Observable consequences (at the Planck scale?); h) What about Gravity? Three alternatives as a start for a brainstorming.