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Nonlinear conductivities of crystals in the independent electron approximation: Results from a velocity gauge analysis
(CFP Room  326, from
20180711 13:30 to
20180711 14:30)

Some formal developments concerning the calculation of nonlinear conductivities of crystals are presented. Even under the simplification of the long wavelength limit and the independent electron approximation, there are subtleties in this calculations, namely on how to deal with particular choices of gauge that define the perturbation. Here, the difficulties inherent to perturbative calculations in the velocity gauge are addressed. In particular, it is shown how, contrary to the common belief in the literature, calculations can be done to any order and for any finite band model in this gauge. The procedure and advantages of the velocity gauge in such calculations are described.

The Analytic Functional Bootstrap I: 1D CFTs and 2D SMatrices
(CFP Room  326, from
20180629 14:00 to
20180629 15:00)

We study a general class of functionals providing an analytic handle on the conformal bootstrap equations in one dimension. We explicitly identify the extremal functionals, corresponding to theories saturating conformal bootstrap bounds, in two regimes. The first corresponds to functionals that annihilate the generalized free fermion spectrum. In this case, we analytically find both OPE and gap maximization functionals proving the extremality of the generalized free fermion solution to crossing. Secondly, we consider a scaling limit where all conformal dimensions become large, equivalent to the large AdS radius limit of gapped theories in AdS2. In this regime we demonstrate analytically that optimal bounds on OPE coefficients lead to extremal solutions to crossing arising from integrable field theories placed in large AdS2

Simplicity in AdS Perturbative Dynamics
(CFP Room  326, from
20180628 15:00 to
20180628 16:00)

We investigate analytic properties of looplevel perturbative dynamics in pure AdS, with the scalar effective theories with nonderivative couplings as a prototype. Explicit computations reveal certain (perhaps unexpected) simplicity regarding the pole structure of the results, in both the Mellin amplitude and a closely related object that we call Mellin preamplitude. Correspondingly we propose a pair of conjectures for arbitrary diagrams at all loops, based on nontrivial evidence up to two loops (and higher loops in a special class of diagrams). We also inspect the structure of residues at poles in the physical channels for several oneloop examples up to a 4point box, as well as a twoloop doubletriangle diagram. These analyses are performed using the recursive construction of Mellin (pre)amplitudes recently prescribed in arXiv:1710.01361, for which we provide detailed derivation and generalization in this paper. Along the way we derive a set of alternative diagrammatic rules for tree (pre)amplitudes, which are better suited to our loop construction. On the mathematical aspect we share some new thoughts on improving the contour analysis of multidimensional Mellin integrals, which are the essential ingredients that make our approach practical.

Analytic Bounds and Emergence of AdS2 Physics from the Conformal Bootstrap
(CFP Room  326, from
20180628 14:00 to
20180628 15:00)

We study the analytic construction of extremal functionals for the 1D conformal Bootstrap crossing equation. This is done with the introduction of the Zhukovsky variable, which increases the domain of convergence of the series expansion of the crossing equation, and then supplemented by contour integrals with certain kernels. The construction is shown to work for integer and halfinteger scaling dimensions of the external operators, which proves a bound that is saturated by the free fermion. We also notice that the limit where the dimension of the external operators becomes large encodes physics of 2D massive Quantum Field Theories and their Smatrices. Finally we use the functionals built in the 1D case to get a nontrivial bound on 2D CFTs.

Gauge covariances and nonlinear optical responses
(CFP Room  326, from
20180620 13:30 to
20180620 14:30)

The formalism of the reduced density matrix is pursued in both length and velocity gauges of the perturbation to the crystal Hamiltonian. The covariant derivative is introduced as a convenient representation of the position operator. This allow us to write compact expressions for the reduced density matrix in any order of the perturbation which simplifies the calculations of nonlinear optical responses; as an example, we compute the first and third order contributions of the monolayer graphene.
Expressions obtained in both gauges share the same formal structure, allowing a comparison of the effects of truncation to a finite set of bands. This truncation breaks the equivalence between the two approaches: its proper implementation can be done directly in the expressions derived in the length gauge, but require a revision of the equations of motion of the reduced density matrix in the velocity gauge.

Entanglement entropy and spacetime
(CFP Room  326, from
20180608 14:00 to
20180608 15:00)

We will review the basic definitions and properties of entanglement entropy, such as positivity, subadditivity and strong subadditivity with explicit example of 3 electrons. We will also review how this property can be calculated in a QFT. After a quick reminder about the brachistochrone problem of extremization, we will give a 'RyuTakayanagi prescription' to calculate 'holographic entanglement entropy(HEE)' for a region in a Large N CFT in terms of a 'certain minimal area in AdS'. We will show that HEE satisfies the usual properties of Entanglement entropy. If time permits, we discuss a reformulation of this prescription and also the higher order corrections in 1/N.

Holography from Conformal Field Theory
(CFP Room  326, from
20180608 10:30 to
20180608 11:30)

We will review the paper 0907.0151, following its original outline. The main idea is to discuss the properties of CFTs which have a bulk dual where locality holds down to the string scale. This is an important feature of AdS/CFT which is seldom tested. We start by reviewing how scattering in local bulk theories leads to special singularities in CFT correlators, and note the properties of CFTs that come from local bulk theories, conjecturing what are the necessary and sufficient conditions for locality in the AdS physics. Then we write general constraints on CFTs with the conjectured properties, and show that the number of possible solutions matches the number of local bulk interactions one can construct. For further credibility of the conjecture, explicit computations in the bulk are matched to particular solutions of the consistency conditions. Finally we will discuss a series of subtleties which are overlooked in the main arguments, and argue that the conclusions hold in general CFTs.

Inflation with Planck data: A survey of some exotic inflationary models
(CFP Room  326, from
20180606 13:30 to
20180606 14:30)

We examine some inflationary models based on modifications of gravity in the light of Planck 2015 data, such as the generalised Chaplygin inspired inflation, models based in N=1 supergravity and braneworld scenarios. We also show that, conversely, potentials with a very flat plateau yield a primordial spectrum similar to that of the Starobinsky model with no need to modify general relativity.

An Ultrametric Route to BerryKeating
(CFP Room  326, from
20180528 13:30 to
20180528 14:30)

A connection between the eigenvalue distribution of an ensemble of random matrices
and the zeroes of the Riemann zetafunction has long been known. A matrix model whose
phase space distribution corresponds to the nontrivial zeroes of the zeta function was recently
proposed. We study matrix models corresponding to the local zetafunctions at each prime and
propose a BerryKeatingtype Hamiltonian from its phase space description. We attempt to
combine this to a Hamiltonian and a matrix model for the Riemann zeta function. (This talk will
be based on work in progress with A. Chattopadhyay, P. Dutta and S. Dutta.)

pAdic AdS/CFT
(CFP Room  326, from
20180523 13:30 to
20180523 14:30)

The pAdic line and its bulk dual, the BrouhatTits tree, is naturally adapted to the holographic dual setting. We will review some recent progress in this area by us and others.