Abstract:

 In the first part I shall be talking about Symmetries of Feynman Integrals. The Symmetries of Feynman Integrals (SFI) is a method for evaluating Feynman Integrals which exposes a novel continuous group associated with the diagram which depends only on its topology and acts on its parameters. Using this method we study the kite diagram (a two-loop diagram with two external legs) and the most general triangle diagram (one-loop diagram with three external legs) with arbitrary masses and space-time dimensions. Generically, this method reduces a Feynman integral into a line integral over simpler diagrams. We identify the locus/loci in parameter space where the integrals further reduce to a mere linear combination of simpler diagrams. We generalize and revisit some known results.

           In the second part I shall speak about Gravitostatic Love Numbers from Membrane Paradigm at large D. Black holes, like any other object - respond to external fields like background electric and gravitational fields. At lowest order, the response of a black hole to, (e.g.) a gravitational wave in the lth spherical harmonic mode is to develop a generalized ‘quadrupole moment’ in the same symmetry channel. The induced moment of the black hole is proportional to the external forcing field. The constant of proportionality between the field and the response is a function of the frequency ω of the incident perturbation. These constants of proportionality are sometimes called ‘Love’ numbers in the study of astrophysical black holes. Using the membrane paradigm, we compute Gravitostatic Love numbers, in large D. This work opens the road of using the membrane paradigm to extend the computation of these Love numbers, for all values of ω in large D.