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Can Teleparallel gravity (TEGR) really be the Translations gauge theory?
(CFP Room (326), from 2018-10-17 13:30 to 2018-10-17 14:30)
I will report on my work reexamining the translation gauge aspect of Teleparallel Equivalent to GR. TEGR is presented as the gravity theory equivalent to GR that is also the gauge theory of translations. We addressed that claim and discovered that it is not tenable given that the principal fiber bundle of translation cannot be built in general and that the need for general frames entails the use of the Lorentz group. We found the solution in a Weitzenbock-Cartan-Poincaré construction that is not yet clearly a gauge theory. This talk is funded by Fundação para a Ciência e a Tecnologia (FCT) through the project UID/FIS/04650/2013.
Planar four-point functions of protected operators in N=4 SYM
(CFP Room (326), from 2018-10-15 13:30 to 2018-10-15 14:30)
We study four-point functions of protected operators in planar N=4 SYM up to the five-loop order. We use a light-cone OPE analysis to constrain the integrands and then fix the integrated correlators with input from integrability. The OPE data we extract allows us to determine the triple wrapping correction in the Hexagon approach to three-point functions, which contributes earlier than expected.
Dark side of the seesaw
(Room 326 (CFP room), from 2018-10-03 14:30 to 2018-10-03 15:30)
I present a model where there is a connection between two apparently uncorrelated sectors, namely neutrino and dark matter. In the model, a scalar field acts as mediator between these two sectors, its vacuum expectation value generating the mass of the dark matter and also taking part in generating neutrino mass. A Z4 symmetry is used, broken by the scalar field vacuum to a remnant Z2 responsible for dark matter stability. The observed light neutrino masses and relic abundance constraint on the dark matter combined lead to predictions of the heavy seesaw scale. This framework to connect dark matter and neutrino sector introduced here is a generic one and can be applied to other possible neutrino mass generation mechanism and different dark matter candidate(s). This talk is funded by Fundação para a Ciência e a Tecnologia (FCT) through the project UID/FIS/04650/2013.
Berry phases and topological physics in one-dimensional systems
(CFP Room - 326, from 2018-07-26 14:00 to 2018-07-26 15:00)
Topological systems are one of the most active research areas in condensed matter physics. The topological characterization of a condensed matter system relies on mathematical constructs such as the Berry phase, the winding number, or the Chern number. In the first part of the talk, I will explain how the Berry phase can be understood as the first cumulant of a series. We calculate higher order cumulants and reconstruct the underlying distribution of the polarization for the Rice-Mele model. Our approach allows the visualization of a topological transition, how a system goes between phases with different quantization. In the second part of the talk, I will go through constructing one-dimensional analogs of the Haldane and Kane-Mele models. In the former, the overall winding number does not indicate topological behavior, but the model falls into two independent Creutz models with opposite windings, and the topological transition occurs within each one separately. The latter ladder model also consists of two Creutz models, one for each spin-channel and falls in the CII symmetry class. In its analysis, the thermodynamic derivation of the generalization of the Streda-Widom formula to the quantum spin Hall effect turned out to be useful.
Extreme Holography
(CFP Room - 326, from 2018-07-25 14:00 to 2018-07-25 15:00)
A massive experimental effort will be devoted in the coming years to the physics of QCD at high energy density and/or high baryon density. Understanding this physics, especially out of equilibrium, is an important theoretical challenge. I will discuss how holography can help us address this challenge. Topics covered will include the far-from-equilibrium dynamics near the QCD critical point and colour superconducting phases. No prior knowledge of string theory required.
Nonlinear conductivities of crystals in the independent electron approximation: Results from a velocity gauge analysis
(CFP Room - 326, from 2018-07-11 13:30 to 2018-07-11 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 S-Matrices
(CFP Room - 326, from 2018-06-29 14:00 to 2018-06-29 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 2018-06-28 15:00 to 2018-06-28 16:00)
We investigate analytic properties of loop-level perturbative dynamics in pure AdS, with the scalar effective theories with non-derivative 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 pre-amplitude. Correspondingly we propose a pair of conjectures for arbitrary diagrams at all loops, based on non-trivial 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 one-loop examples up to a 4-point box, as well as a two-loop double-triangle 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 multi-dimensional 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 2018-06-28 14:00 to 2018-06-28 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 half-integer 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 S-matrices. Finally we use the functionals built in the 1D case to get a non-trivial bound on 2D CFTs.
Gauge covariances and nonlinear optical responses
(CFP Room - 326, from 2018-06-20 13:30 to 2018-06-20 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.