Quantum Fields and Strings

I will discuss constraints on the S-matrix of gapped, Lorentz invariant quantum field theories due to crossing symmetry, analyticity and unitarity.  In particular I will bound cubic couplings, quartic couplings and scattering lengths relevant for the elastic scattering amplitude of two identical scalar particles. After a warm-up in 1+1 dimensions I will move to 3+1 dimensions.  In the cases where the results can be compared with results in the older S-matrix literature they are in excellent agreement.

We derive constraints on the operator product expansion of two stress tensors in conformal field theories (CFTs). In large N CFTs with a large gap to single-trace higher spin operators, we show that the coupling of two stress tensors to other single-trace operators ("TTO") is suppressed by powers of the higher spin gap, dual to the mass scale of higher spin particles in AdS. The absence of light higher spin particles is thus a necessary condition for the existence of a consistent truncation to general relativity in AdS. We are led to propose that, in general, the inverse gap scale is the CFT "dual" of an AdS derivative in a classical action. These results are derived by imposing unitarity on mixed systems of spinning four-point functions in the Regge limit. Using the same method, but without imposing a large gap, we derive new inequalities on TTO-type couplings valid in any CFT.

Many researchers have been studying the time evolution of entanglement entropy in the sudden quenches where a characteristic mass scale suddenly changes. It is well-know that in these quenches, the change of entanglement entropy become thermal entropy which is proportional to a subsystem size in the late time. However, we do not know which quenches thermalize a subsystem. In our works, we have been studied the time evolution of quantum entanglement in the global quenches with finite quench rate (smooth quenches). Thus, we found that diabaticity plays an important role, so that quenches thermalize the subsystem.

Gravitational shockwaves may signal the breakdown of effective field theory near black hole horizons. Motivated by this, I will revisit the Dray-‘t Hooft solution and explain how to generalize it to the Kerr-Newman background. In doing so I will emphasize the method of spin coefficients (the Newman-Penrose formalism) in its compacted form (the Geroch-Held-Penrose formalism).

In this talk I prove that the standard notion of entanglement is not defined for gravitationally anomalous two-dimensional theories  because they do not admit a local tensor factorization of the Hilbert space into local Hilbert spaces.  I make this precise by combining two observations:

    First, a two-dimensional CFT admits a consistent quantization on a space with boundary only if it is not anomalous.

    Second, a local tensor factorization always leads to a definition of consistent, unitary, energy-preserving boundary condition.

    As a corollary we establish a generalization of the Nielsen--Ninomiya theorem to all two-dimensional unitary local QFT:

    No continuum quantum field theory in two dimensions can admit a lattice regulator unless its gravitational anomaly vanishes.

I also show that the conclusion can be generalized to six dimensions by dimensional reduction on a four-manifold of nonvanishing signature.  I will advocate that these points be used to reinterpret the gravitational anomaly quantum-information-theoretically, as a fundamental obstruction to the localization of quantum information.

Quantum-critical strongly correlated systems feature universal collision-dominated collective transport. Viscous electronics is an emerging field dealing with systems in which strongly interacting electrons flow like a fluid. I shall describe recent theoretical and experimental results: negative resistance, current vortices, expulsion of electric field, conductance exceeding the fundamental quantum-ballistic limit and other wonders of viscous electronics.

Nature Physics 2016, 2017,  PNAS 2017,  PhysRevLet 2017

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.

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

I will describe a holographic solution corresponding to a traversable wormhole in AdS/CFT.  The construction involves directly coupling the boundary CFT's, and corresponds to chaos-facilitated quantum teleportation between the two sides.  It does not violate boundary causality or other fundamental physics principles.

Known N=4 theories in four dimensions are characterized by a choice of gauge group, and in some cases some "discrete theta angles", as classified by Aharony, Seiberg and Tachikawa. I will review how this data, for the theories with algebra su(N), is encoded in various familiar realizations of the theory, in particular in the holographic AdS_5 \times S^5 dual and in the compactification of the (2,0) A_N theory on T^2. I will then show how the resulting structure, given by a choice of polarization of an appropriate cohomology group, admits additional choices that, unlike known theories, generically preserve SL(2,Z) invariance in four dimensions.

I discuss some aspects of boundary conformal field theories (bCFTs). I will demonstrate that free bCFTs have a universal way of satisfying crossing symmetry constraints. I will introduce a simple class of interacting bCFTs where the interaction is restricted to the boundary. Finally, I will discuss relationships between boundary trace anomalies and boundary limits of stress-tensor correlation functions.