Scientific Series

We discuss a candidate mechanism through which one might address the various cosmological constant problems. We observe that the renormalization of gravitational couplings manifests non-local modifications to Einstein's equations as quantum corrected equations of motion, and in doing so offers a complimentary realization of the degravitation paradigm-- a realization through which its non-linear completion and the corresponding modified Bianchi identities are readily understood. We proceed to consider theories whose coupling to gravity might a priori induce non-trivial RG flow for gravitational couplings in the IR, and arrive at a class of non-local effective actions which yield a suitably degravitating filter function for Newton's constant upon subsequently being integrated out.

One might have hoped that philosophers had sorted out what ‘truth’ is supposed to be by now. After all, Aristotle offered what seems to be a clear and simple characterization in his Metaphysics. So perhaps it is surprising (and then again perhaps it isn’t), that contemporary philosophers have not settled on a consensus regarding the nature of truth to this day. In fact, the most obvious theory of truth, that truth consists in correspondence to the facts, seems to be steadily waning in popularity in technical circles, replaced instead by a perhaps puzzlingly austere minimalist theory that restricts its characterization of truth to the familiar equivalence schema:

is true if and only if p. The differences between such deflationary theories and the ‘traditional’ correspondence theory of truth, and perhaps even more strikingly between these theories and epistemic theories of truth, call to mind counterpart features in different attitudes about the proper interpretation of quantum mechanics. By reviewing the most striking features of different theories of truth, as well as some of their most difficult objections, we can start to see where different interpretations seem to be reliant on (or at least quite congenial to) particular theories of truth and also where these theories begin to reveal themselves as variously helping and hindering the smooth functioning of different interpretations.

Coincident detections of electromagnetic and gravitational wave signatures from the merger of supermassive binary black holes are the next observational grand challenge. Such detections will provide a wealth of opportunities to study gravitational physics, accretion physics, and cosmology. Understanding the conditions under which coincidences of electromagnetic and gravitational wave signatures arise during supermassive black hole mergers is therefore of paramount importance, requiring multi-scale/physics computational modeling. I will given an overview of these numerical studies and in particular focus on our effort to model the merger of supermassive black hole binaries in the presence of gaseous environments.

We study a novel state of matter: algebraic Bose liquid (ABL). An ABL is a quantum bosonic system on a 2d or 3d lattice that does not break any symmetry in its ground state, but still able to stabilize a gapless spectrum. At high energy these boson systems only have the simplest U(1) global symmetry associated with the conservation of boson number, but at low energy the system is described by self-dual gauge fields. In this talk we will present two new ABL phases emerged from a quantum Boson model on the cubic lattice. At low energy these two ABL phases are described by the linearized z=2 and z=3 Lifshitz gravity respectively. We will show that the self-duality of the field theory is crucial to guarantee the stability of the ABL. References: Cenke Xu, arXiv:cond-mat/0602443, Phys. Rev. B. 74, 224433 Cenke Xu and Petr Horava, arXiv:1003.0009

After prodigious work over several decades, binary black hole mergers can now be simulated in fully nonlinear numerical relativity. However, these simulations are still restricted to mass ratios q = m2/m1 > 1/10, initial spins a/M < 0.9, and initial separations r/M < 10. Fortunately, analytical techniques like black-hole perturbation theory and the post-Newtonian approximation allow us to study much of this region in parameter space that remains inaccessible to numerical relativity. I will use black-hole perturbation theory to establish a fundamental upper limit to the final spin that can be attained through binary mergers, and show how this limit can be used to improve predictions of final spins for finite mass ratios as well. I will also show that post-Newtonian inspirals between 1000 M < r < 10 M can align or anti-align black hole spins with each other, dramatically changing the distributions of final spins and recoil velocities that would be expected in astrophysical black hole mergers.

For the past century, there has been much discussion and debate about the equations of motion satisfied by a classical point charge when the effects of its own electromagnetic field are taken into account. Derivations by Abraham (1903), Lorentz (1904), Dirac (1938) and others suggest that the "self-force" (or "radiation reaction force") on a point charge is given in the non-relativistic limit by a term proportional to the time derivative of the acceleration of the charge. However, the resulting equations of motion then become third order in time, and they admit highly unphysical "runaway" solutions. During the past century, there also has been much discussion and debate about the interpretation of these equations of motion and the conditions that can/should be imposed to eliminate the runaway behavior. We argue that the above difficulties stem from that fact that the usual notion of a point charge is mathematically ill defined. However, a mathematically rigorous notion of a point charge arises in a perturbative description of a body if one considers a limit wherein not only the size of a body but its charge and mass go to zero in an asymptotically self-similar manner. We show how the Abraham-Lorentz-Dirac self-force then arises in a perturbative description of the body's motion, but does not give rise to runaway behavior. As a biproduct of this work, we also rigorously derive dipole forces and resolve some paradoxes of elementary physics, such as how a magnetic dipole placed in a non-uniform magnetic field can gain kinetic energy despite the fact that the magnetic field can "do no work" on the body.

Recently, a new class of topological states has been theoretically predicted and experimentally realized. The topological insulators have an insulating gap in the bulk, but have topologically protected edge or surface states due to the time reversal symmetry. In two dimensions the edge states give rise to the quantum spin Hall (QSH) effect, in the absence of any external magnetic field. I shall review the theoretical prediction[1] of the QSH state in HgTe/CdTe semiconductor quantum wells, and its recent experimental observation[2]. The edge states of the QSH state supports fractionally charged excitations[3]. The QSH effect can be generalized to three dimensions as the topological magneto-electric effect (TME) of the topological insulators[4]. Bi2Te3, Bi2Se3 and Sb2Te3 are theoretically predicted to be topological insulators with a single Dirac cone on the surface[5]. I shall present a realistic experimental proposals to observe the magnetic monopoles on the surface of topological insulators[6]. Topological superconductors and superfluid have been theoretically proposed recently [7], in both two and three dimensions. They have a full pairing gap in the bulk, and their mean field Hamiltonian look identical to that of the topological insulators. However, the gapless surface states consists of a single Majorana cone, containing only half the degree of freedom compared to the single Dirac cone on the surface of a topological insulators. I shall discuss their physics properties and the search for these novel states in real materials. [1] A. Bernevig, T. Hughes and S. C. Zhang, Science, 314, 1757, (2006) [2] M. Koenig et al, Science 318, 766, (2007) [3] J. Maciejko, Chaoxing Liu, Yuval Oreg, Xiao-Liang Qi, Congjun Wu, and Shou-Cheng Zhang, , Phys. Rev. Lett. {\bf 102}, 256803 (2009). [4] Xiao-Liang Qi, Taylor Hughes and Shou-Cheng Zhang, Phys. Rev B. 78, 195424 (2008) [5] Haijun Zhang, Chao-Xing Liu, Xiao-Liang Qi, Xi Dai, Zhong Fang, and Shou-Cheng Zhang, Nature Physics 5, 438 (2009). [6] Xiao-Liang Qi, Run-Dong Li, Jiadong Zang and Shou-Cheng Zhang, Science 323, 1184 (2009). [7] Xiao-Liang Qi, Taylor L. Hughes, Srinivas Raghu and Shou-Cheng Zhang, Phys. Rev. Lett. 102, 187001 (2009)

Our starting point is a particular `canvas' aimed to `draw' theories of physics, which has symmetric monoidal categories as its mathematical backbone. With very little structural effort (i.e. in very abstract terms) and in a very short time this categorical quantum mechanics research program has reproduced a surprisingly large fragment of quantum theory. Philosophically speaking, this framework shifts the conceptual focus from `material carriers' such as particles, fields, or other `material stuff', to `logical flows of information', by mainly encoding how things stand in relation to each other. These relations could, for example, be induced by operations. Composition of these relations is the carrier of all structure. Thus far the causal structure has been treated somewhat informally within this approach. In joint work with my student Raymond Lal, by restricting the capabilities to compose, we were able to formally encode causal connections. We call the resulting mathematical structure a CauCat, since it combines the symmetric monoidal stricture with Sorkin's CauSets within a single mathematical concept. The relations which now respect causal structure are referred to as processes, which make up the actual `happenings'. As a proof of concept, we show that if in a quantum teleportation protocol one omits classical communication, no information is transfered. We also characterize Galilean theories. Classicality is an attribute of certain processes, and measurements are special kinds of processes, defined in terms of their capabilities to correlate other processes to these classical attributes. So rather than quantization, what we do is classicization within our universe of processes. We show how classicality and the causal structure are tightly intertwined. All of this is still very much work in progress!

We apply newly-developed techniques for studying perturbative scattering amplitudes to gauge theories with matter. It is well known that the N=4 SYM theory has a very simple S-matrix; do other gauge theories see similar simplifications in their S-matrices? It turns out the one-loop gluon S-matrix simplifies if the matter representations satisfy some group theoretic constraints. In particular, these constraints can be expressed as linear Diophantine equations involving the higher order Indices (or higher-order Casimirs) of these representations. We solve these constraints to find examples of theories whose gluon scattering amplitudes are as simple as those of the N=4 theory. This class includes the N=2, SU(K) theory with a symmetric and anti-symmetric tensor hypermultiplet. Non-supersymmetric theories with appropriately tuned matter content can also see remarkable simplifications. We find an infinite class of non-supersymmetric amplitudes that are cut-constructible even though naive power counting would suggest the presence of rational remainders.

Gamma rays from WIMP annihilation are an important signal through which we search for non-gravitational interactions of dark matter. In particular, lines in the energy spectrum of gamma rays provide a signal which is difficult for conventional astrophysics to fake, and are thus promising despite the fact that such lines are generically expect to be suppressed, arising from one loop processes. I will discuss two theories which have an interesting family of gamma ray lines and discuss how such lines can reveal information about the WIMPs and the dark sector.

A quantum theory of gravity implies a quantum theory of geometries. To this end we will introduce different phases spaces and choices for the space of discretized geometries. These are derived through a canonical analysis of simplicity constraints - which are central for spin foam models - and gluing constraints. We will discuss implications for spin foam models and map out how to obtain a path integral quantization starting from a canonical quantization.