Quantum Fields and Strings

We look at the interior operator reconstruction from the point of view of Petz map and study its complexity. We show that Petz maps can be written as precursors under the condition of perfect recovery. When we have the entire boundary system its complexity is related to the volume / action of the wormhole from the bulk operator to the boundary. When we only have access to part of the system, Python's lunch appears and its restricted complexity depends exponentially on the size of the subsystem one loses access to.

I describe a novel way to produce states associated to geodesic motion for classical particles in the bulk of AdS that arise from particular operator insertions at the boundary

at a fixed time. When extended to black hole setups, one can understand how to map back the geometric information of the geodesics back to 

the properties of these operators. In particular, the presence of stable circular orbits in global AdS are analyzed. The classical Innermost Stable Circular Orbit 

(ISCO) play an important role separating metastable state excitations from those that quickly  fall in the horizon of  black hole. In the dual CFT, this metastability effect must be a non-perturbative effect due to the curvature on the boundary.

I will explain that a geometric theory built upon the theory of complex surfaces can be used to understand wide variety of phenomena in five-dimensional supersymmetric theories, which includes the following:

1. Classification of 5d superconformal field theories (SCFTs).
2. Enhanced flavor symmetries of 5d SCFTs.
3. 5d N=1 gauge theory descriptions of 5d and 6d SCFTs.
4. Dualities between 5d N=1 gauge theories.
5. T-dualities between 6d N=(1,0) little string theories.

This relationship between geometry and 5d theories is based on M-theory and F-theory compactifications.

I will describe how within eleven dimensional supergravity one can compute the logarithmic correction to the Bekenstein-Hawking entropy of certain magnetically charged asymptotically AdS_4 black holes with arbitrary horizon topology.  The result perfectly agrees with the dual field theory computation of the topologically twisted index in  ABJM theory and in certain theories obtained from M5 wrapping a hyperbolic 3-manifold. The extension to rotating, electrically charged AdS_4 black holes and the dual superconformal index will also be discussed. 

For any vertex operator algebra V, Y. Zhu constructed an associative algebra Zhu(V) that captures its representation theory (more generally, given a finite order automorphism g of V, there exists an algebra Zhu_g(V) that captures g-twisted representation theory of V). 

To a 4d N=2 superconformal theory T, one assigns a vertex algebra V[T] by the construction of Beem et al. We explain one role of Zhu algebra in this context. Namely, we show that a certain quotient of the Zhu algebra describes what happens to the Schur sector of the theory T under the dimensional reduction on S^1. This connects the VOA construction in 4d N=2 SCFT to the topological quantum mechanics construction in 3d N=4 SCFT, with the latter being given by the aforementioned quotient of the Zhu algebra. In the process, we will discuss how to reformulate the VOA construction on an S^3 x S^1 geometry.

We study the defect operator product expansion (OPE) of displacement operators in free and interacting conformal field theories using replica methods. We show that as n approaches 1 a contact term can emerge when the OPE contains defect operators of twist d−2. For interacting theories and general states we give evidence that the only possibility is from the defect operator that becomes the stress tensor in the n→1 limit. This implies that the quantum null energy condition (QNEC) is always saturated for CFTs with a twist gap. As a check, we show independently that in a large class of near vacuum states, the second variation of the entanglement entropy is given by a simple correlation function of averaged null energy operators as studied by Hofman and Maldacena. This suggests that sub-leading terms in the the defect OPE are controlled by a defect version of the spin-3 non-local light ray operator and we speculate about the possible origin of such a defect operator. For free theories this contribution condenses to a contact term that leads to violations of QNEC saturation.

In this talk I will review the state of the art in PN gravity, and in particular its significant advancement via the EFT of spinning gravitating objects. First, I will introduce the concept of a tower of EFTs for the binary inspiral problem. I will then present the intricate formulation of the EFT of spinning objects. Finally, I will present some advanced results accomplished within this framework.

We propose a unified manner of understanding two important phenomena: color confinement in large-N gauge theory, and Bose-Einstein condensation (BEC). We do this by clarifying the relation between the standard criteria, based on the off-diagonal long range order (ODLRO) for the BEC and the Polyakov loop for gauge theory: the constant offset of the distribution of Polyakov line phase is ODLRO. Indistinguishability associated with the symmetry group --- SU(N) or O(N) in gauge theory, and S_N permutation in the system of identical bosons --- plays the key role in both cases. This viewpoint may have implications to confinement at finite N, and to quantum gravity via gauge/gravity duality. 

The elliptic genus is a powerful deformation invariant of 1+1D SQFTs: if it is nonzero, then it protects the SQFT from admitting a deformation to one with spontaneous supersymmetry breaking. I will describe a "secondary" invariant, defined in terms of mock modularity, that goes beyond the elliptic genus, protecting SQFTs with vanishing elliptic genus. The existence of this invariant supports the hypothesis that the space of minimally supersymmetric 1+1D SQFTs provides a geometric model for universal elliptic cohomology. Based on joint works with D. Gaiotto and E. Witten.

In order to satisfy the Reeh-Schlieder theorem, I study the infinite-dimensional Hilbert spaces using von Neumann algebras. I will first present the theorem that the entanglement wedge reconstruction and the equivalence of relative entropies between the boundary and the bulk (JLMS) are exactly identical. Then I will demonstrate the entanglement wedge reconstruction with a tensor network model of von Neumann algebra with type II1 factor, which guarantees the equivalence between the boundary and the bulk. I will further sketch that this toy model can be generalized to provide more general von Neumann algebras, including the case of a type III1 factor. This can give further insights to understanding quantum gravity from an algebraic perspective.

Subregion duality is an idea in holography which states that every subregion of the boundary theory has a corresponding subregion in the bulk theory, called the 'entanglement wedge', to which it is dual. In the classical limit of the gravity theory, we expect the fields in the entanglement wedge to permit a Hamiltonian description involving a phase space and Poisson brackets. In this talk, I will describe how this phase space arises from the point of view of the boundary theory. In particular, I will explain how it emerges from measurements of a certain quantum information-theoretic quantity known as the 'Uhlmann phase', in the boundary subregion.

The Monster CFT is a (1+1)d holomorphic CFT with the Monster group global symmetry.  The symmetry twisted partition functions exhibit the celebrated Monstrous Moonshine Phenomenon.  From a modern point of view, topological defects generalize the notion of global symmetries.  We argue that the Monster CFT has a Kramers-Wannier duality defect that is not associated with any global symmetry. The duality defect extends the Monster group to a larger category of topological defects that contains an Ising subcategory.  We introduce the defect McKay-Thompson series defined as the Monster partition function twisted by the duality defect, and find that it is invariant under the genus-zero congruence subgroup 16D0 of PSL(2,Z).