Scientific Series

In general relativity causal relations between any pair of events is uniquely determined by locally predefined variables - the distribution of matter-energy degrees of freedom in the events' past light-cone. Under the assumption of locally predefined causal order, agents performing freely chosen local operations on an initially local quantum state cannot violate Bell inequalities. However, superposition of massive objects can effectively lead to "entanglement" in the temporal order between groups of local operations, enabling the violation of the inequalities. This shows that temporal orders between events can be "indefinite" in non-classical space-times.

Carefully studying the singularity structure of the moduli space of vacua of super conformal field theories, provides an incredibly powerful tool to extract information about such theories. In particular I will outline a concrete, yet technically challenging, strategy to go about carrying out a classification for SCFTs with extended supersymmetry in 4d.

I will explain in details how this classification has been worked out successfully for N=2 SCFTs in rank-1 and it is very promising in rank-2. And how with even higher Supersymmetry (N≥3) we can obtain a classification valid for all ranks making a few reasonable, yet key, assumptions.

Making perturbative quantum field theory (QFT) mathematically rigorous is an important step towards understanding how the non-perturbative framework should look like. Recently, two approaches have been developed to address this issue: perturbative algebraic quantum field theory (pAQFT) and the factorization algebras approach developed by Costello and Gwilliam. The former works primarily in Lorentzian signature, while the later in Euclidean, but there are many formal parallels between them. In this talk I will show the recent results relating these two frameworks and discuss the consequences for future research (joint work with Gwilliam).

The Hilbert space of a theory with diffeomorphism symmetry does not factorize into spatial subregions due to gauge constraints. This presents a challenge for defining a notion of entanglement entropy associated with a subregion in these theories. In this talk, I will describe the extended phase space method of Donnelly and Freidel for handling this nonfactorization. It involves introducing edge modes living at the boundary of the subregion, whose purpose is to restore the diffeomorphism invariance that was broken by the subregion's presence. These edge modes are then expected to contribute to the subregion's entanglement entropy. I will further discuss the relevance of the edge mode entanglement to the entropy of black holes, where it may provide a statistical interpretation of the Wald entropy within the low energy effective description.

Quantum gravity has many conceptual problems. Amongst the most well-known is the "Problem of Time": gravitational observables are global in time, while we would really like to obtain probabilities for processes taking us from an observable at one time to another, later one. Tackling these questions using relationalism will be the preferred strategy during this talk. The 'relationalist' approach leads us to shed much redundant information and enables us to identify a reduced configuration space as the arena on which physics unfolds, a goal still beyond our reach in general relativity. Moreover, basing our ontology on this space has far-reaching consequences. One is that it suggests a natural interpretation of quantum mechanics; it is a form of ‘Many-Worlds’ called Many-Instant QM. Another is that the gravitational reduced configuration space has a rich, highly asymmetric structure which singles out preferred, non-singular and homogeneous initial conditions for a wave-function of the universe, which is yet to be explored.   

We establish a direct connection between scattering amplitudes for bi-adjoint scalar theories and a classic polytope--the "associahedron"--known to mathematicians since the 1960s. We find an associahedron naturally living in kinematic space. The tree level scattering amplitude is simply a geometric invariant of the associahedron called its "canonical form" [2], which is a differential form on kinematic space with logarithmic singularities on the boundaries of the associahedron. We show that basic physical principles like locality and unitarity are "rediscovered" as properties of the geometry, and certain "soft" limits can be converted to geometric statements as well.

The associahedron in kinematic space plays an important role in the context of scattering equations. We discover that the scattering equations act as a diffeomorphism between the interior of the open string moduli space (yet another associahedron) and the associahedron in kinematic space. This observation provides the key to a novel derivation of the bi-adjoint CHY formula. Finally, we emphasize the importance of the scattering amplitude as a differential form, as suggested by the "canonical form" construction. We argue on general grounds that every color-dressed amplitude is dual to a form on kinematic space. This is motivated by the surprising observation that "projective" forms on kinematic space satisfy Jacobi identities and therefore have novel implications for color-kinematics duality.

References:

[1] Nima Arkani-Hamed, Yuntao Bai, Song He & Gongwang Yan. In preparation.

[2] Nima Arkani-Hamed, Yuntao Bai & Thomas Lam. Positive Geometries and Canonical Forms. arXiv 1703.04541

The radial acceleration relation is an empirical universal scaling relation between the total gravitational field and the Newtonian acceleration generated by baryons at any given radius within spiral galaxies. In this talk, I will discuss the possibility that such a relation arises from interactions between baryons and dark matter (DM), rather than from feedback processes or modifications of gravity. Starting from this premise, I will discuss what we can infer about the nature of baryon-DM interactions. In particular, I will argue that  such interactions must depend on the local DM density in order to correctly reproduce the observed behavior of spiral and elliptical galaxies. I will briefly revisit existing phenomenological, astrophysical and cosmological constraints on baryon-DM interactions in light of the unusual density dependence of our cross-section. I will conclude by mentioning possible ways of realizing this scenario in particle physics models, and discuss a non-relativistic toy model.

I will describe our recent work from 1709.07460, where we introduce a new renormalization group algorithm for tensor networks. The algorithm is based on a novel understanding of local correlations in a tensor network, and a simple method to remove such correlations from any network. It performs comparably with the best competing algorithms on 2D/(1+1)D systems, but is significantly simpler to implement, and easier to generalize to different lattices and graphs, including to higher dimensions. I will begin the talk by discussing renormalization group methods for tensor networks in general, then describe our algorithm and its advantages, show some benchmark results, and finally comment on the status of implementing real-space renormalization for 3D tensor networks.

The much-anticipated joint detection of gravitational waves and electromagnetic radiation was achieved for the first time on August 17, 2017, for the binary neutron star merger GW170817.  This event was detected by Advanced LIGO/Virgo, gamma-ray satellites, and dozens of telescopes on the ground and in space spanning from radio to X-rays.  In this talk I will describe the exciting discovery of the optical counterpart, which in turn led to several detailed studies across the electromagnetic spectrum.  The results of the observations carried out by our team include the first detailed study of a "kilonova", an optical/infrared counterpart powered by the radioactive decay of r-process nuclei synthesized in the merger, as well as the detection of an off-axis jet powering radio and X-ray emission.  These results provide the first direct evidence that neutron star mergers are the dominant site for the r-process and are the progenitors of short GRBs.  I will also describe how studies of the host galaxy shed light on the merger timescale, and describe initial constraints on the Hubble Constant from the combined GW and EM detection.        

In this talk I will define the quantum K-theory of Nakajima quiver varieties and show its connection to representation theory of quantum groups and quantum integrable systems on the examples of the Grassmannian and the flag variety. In particular, the Baxter operator will be identified with operators of quantum multiplication by quantum tautological classes via Bethe equations. Quantum tautological classes will also be constructed and, time permitting, an explicit universal combinatorial formula for them will be shown.
Based on joint works with P.Koroteev, A.Smirnov and A.Zeitlin