Scientific Series

Topological quantum computation is based on the possibility of the realization of some TQFTs in Nature as topological phases of quantum matter.  Theoretically, we would like to classify topological phases of matter, and experimentally, find non-abelian objects in Nature.  We will discussion some progress for a general audience.

 

In this talk we will discuss how C*-algebras can be identified and characterised in terms of certain cosheaves with self-action. The reason we are interested in such a study is it to try and give a rigorous mathematical derivation of the axioms of quantum theory. In particular, many of the standard axioms for C*-algebras have unclear physical and operational meaning, but by defining an equivalence of categories between C*-algebras and cosheaves with self-action, we believe that these axioms can acquire a clear operational meaning. So far, however, we have only managed to show that every C*-algebra becomes a cosheaf with self-action, but we don't know whether the converse holds as well. This work is done in collaboration with Tobias Fritz.

I will describe entanglement entropy of a cap-like region for a generic quantum field theory residing in the Bunch-Davies vacuum on de Sitter space. Entanglement entropy in this setup is identical with the thermal entropy in the static patch of de Sitter, and it is possible to derive a simple relation between the vacuum expectation value of the energy-momentum tensor trace and the RG flow of entanglement entropy. In particular, renormalization of the cosmological constant and logarithmic divergence of the entanglement entropy are interrelated in this setup. These findings are confirmed by recovering known universal contributions for a free field theory deformed by a mass operator as well as correct universal behaviour at the fixed points. In three dimensions the renormalized entanglement entropy is stationary at the fixed points but not monotonic. Computational evidence that the universal `area law' for a conformally coupled scalar is different from the known result in the literature will be given, and I will argue that this difference survives in the limit of flat space.

The search for physics beyond the Standard Model at the LHC is largely oriented towards new particles associated with solutions to the electroweak hierarchy problem. While the precise character of these partner states may vary from model to model, they typically possess large QCD production rates favorable for detection at hadron colliders. Null results in searches for partner particles during Run 1 of the LHC have placed the idea of electroweak naturalness under increasing strain. In this talk I'll discuss a broad class of natural theories where the new degrees of freedom relevant for naturalness lie in hidden sectors and are largely unconstrained by LHC data. Rather than rendering electroweak naturalness untestable, they give rise to entirely new signs of naturalness at the LHC, including displaced decays and other exotic signatures. They also furnish a variety of viable dark matter candidates testable at current and future experiments.

I will talk about a novel theory of dark matter superfluidity that matches the success of LCDM model on cosmological scales while simultaneously reproducing the MOND phenomenology on galactic scales.

In this talk I will discuss the most singular point and T^2 compactifications of a 6d N=(1,0) supersymmetric conformal field theory (SCFT) which arises as the worldvolume theory on coincident N of M5 branes probing the singular locus of the ALE orbifold. When N=1, the compactified theory can be describe by a class S theory of three punctured sphere. Generalization to multiple M5s case results in a pair of 4d N=2 SCFTs which are connected by a IR free gauge multiplet. Along the line, we see that the “dynamical version" of class S simple puncture plays a role. Closing one of two flavor groups, we can isolate one of them with manifest SL(2,Z) invariance of T^2 and a non-abelian flavor group, including presumably new N=2 SCFTs.

 I  will first analytically show a simple, yet subtle "invariance" of two-body decay kinematics for the case of a massless  daughter and a mother particle which is unpolarized and has a *generic* boost distribution in the laboratory frame. Namely, the laboratory frame energy distribution of the massless decay product has a peak, whose location is identical to the  (fixed) energy of that particle in the rest frame of the corresponding mother particle. In turn, this value of the energy is a simple function of the other masses involved in the decay.
As a proof of principle of the usefulness of this observation, I will then apply it for measuring  the mass of the top quark at the LHC, using simulated data (including experimental  effects). In fact, CMS collaboration (in CMS-PAS-TOP-15-002) has recently implemented our method for measuring the top quark mass! Finally, I will show how it can be used to measure all the superpartner masses in a cascade decay chain of the gluino.

The Hartle-Hawking (HH) no-boundary proposal provides a Euclidean path integral prescription for a measure on the space of all possible initial conditions. Apart from  saddle point  and  minisuper-space calculations, it is hard to obtain results using the unregulated path integral. A promising choice of spacetime  regularisation comes from the causal set (CST) approach to quantum gravity.  Using analytic results as well as Markov Chain Monte Carlo and numerical integration methods we obtain  the HH wave function in a theory of non-perturbative 2d CST. We find that the  wave function is sharply peaked with the peak geometry changing discretely with "temperature". In the low temperature regime the peak corresponds to causal sets which have no continuum counterpart but exhibit physically interesting behaviour. They show a rapid spatial expansion with respect to the discrete proper time as well as  a high degree of spatial homogeneity due to extensive overlap of the causal past. While our results are limited to 2 dimensions they provide a concrete example of how quantum gravity could explain the initial conditions for our observable universe.

I'll discuss the two topological twists of 3d N=4 theories, and explain how to understand them in the AKSZ/BV formalism, and how they relate to twists of 4d N =2 theories.  Symplectic duality then takes the form of an equivalence between 3d N=4 theories which interchanges the two topological twists.  I'll also introduce monopole operators and explain the role they play in symplectic duality.

In this talk I will describe numerical constructions of gravitational
duals of theories deformed by localized Dirac delta sources for scalar
operators. We perform two different constructions, one at zero and
the other at nonzero temperature. Surprisingly we find that imposing the preservation of scale
invariance at zero temperature requires the bulk scalar self-interaction potential to be
the one found in a certain Kaluza-Klein compactification of 11D supergravity.
The gravitational setup seems a-priori to be quite unusual and challenging
from the numerical relativity perspective.

Topological aspects of physical systems, including the called topological states of matter, have become hot topics in the frontiers of physics in recent years. Here I would like to present a mathematically "popular" talk for professional physicists for a highlight or overview of how one can systematize knowledge of topological aspects of quantum field theories. Our starting points are Descent Equations and Gauge Structure in Configuration Space in Field Theory. (The audience needs only to know the meaning of "differential forms".)

We derive the constitutive relations of first order charged hydrodynamics for theories with Lifshitz scaling and broken parity in 2+1 and 3+1 spacetime dimensions. In addition to the anomalous (in 3+1) or Hall (in 2+1) transport of relativistic hydrodynamics, there is an additional non-dissipative transport allowed by the absence of boost invariance. We analyze the non-relativistic limit and use a phenomenological model of a strange metal

to argue that these effects can be measured in principle by using electromagnetic fields with non-zero gradients.