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I am a theoretical physicist with interests in effective field theory, particle physics, and cosmology, as well as formal aspects of scattering amplitudes, holography, and conformal field theory.
A Bottom-Up Approach to AdS/CFT, and Holography in Flat Spacetime
Due to the equivalence principle of General Relativity, spacetime only exists as a redundancy of description in theories that unite Quantum Mechanics with Gravity. Precisely well-defined observables in Quantum Gravity must therefore be associated with the `boundary' of spacetime, at infinity. The AdS/CFT correspondence explicitly manifests this Holographic Principle.
A major focus of my research has been the pursuit of a detailed, bottom-up understanding of holography. At a very practical level, one can study general effective field theories (EFTs) in AdS spacetime in order to understand the phenomena and the limitations of bulk EFT in the language of the boundary CFT. Furthermore, by studying CFT processes dual to bulk scattering in the limit that the AdS curvature becomes vanishingly small, we obtain a holographic theory for the flat spacetime S-Matrix.
In A Natural Language for AdS/CFT Correlators, with Fitzpatrick, Penedones, Raju, and Van Rees, we showed that Mellin Space is to CFT Correlation functions as Momentum Space is to flat space Scattering Amplitudes. Most importantly, we showed that CFT correlation functions factorize on poles in Mellin space, and we used this property to derive algebraic Feynman rules for AdS/CFT. This new development trivializes many calculations that would otherwise be completely intractable.
In Analyticity and the Holographic S-Matrix and Unitarity and the Holographic S-Matrix, both with A.L. Fitzpatrick, we derived a very simple and natural formula that expresses the flat spacetime S-Matrix in terms of boundary CFT correlation functions in the Mellin representation. We demonstrate the formula with some newly computable tree and loop amplitudes from AdS, explaining how the analyticity properties of scattering amplitudes arise from the poles of CFT correlators in Mellin space. In the Unitarity paper, we derive the usual Optical Theorem and Cutting Rules from the OPE in the holographically dual CFT. Finally, we derive a simple formula relating OPE coefficients to scattering amplitudes at all energies, showing how one could use simple and standard CFT data to understand Black Hole evaporation exactly.
In AdS Field Theory from Conformal Field Theory, with A.L. Fitzpatrick, we gave necessary and sufficient conditions for a CFT to have a dual description in terms of an Effective Field Theory in AdS. We also explained how the exchange of `virtual particles' in AdS follows from the exchange of operators in CFT correlators, providing a constructive method for obtaining an AdS theory dual to the CFT.
In The Analytic Bootstrap and AdS Superhorizon Locality, with Fitzpatrick, Poland, and Simmons-Duffin, we used the bootstrap to show that all CFTs in three or more dimensions can be viewed as local theories at large distances in AdS. This is a more physical way of saying that products of operators have a sort of perturbative expansion at large spin.
A New S-Matrix Program
Scattering Amplitudes are far simpler than the Feynman diagrams we have traditionally used to compute them. One might hope that this offers a clue related to the holographic description of flat spacetime, or at the very least, a different way of thinking about Quantum Field Theory. Advances in the computation of scattering amplitudes have practical use, as we need many non-trivial loop-level cross sections in QCD for the study of LHC physics.
In On Tree Amplitudes in Gauge Theory and Gravity with N. Arkani-Hamed, we gave a very general explanation/derivation/proof of the BCFW Recursion Relations, which allow for an extremelly efficient and purely on-shell (and therefore `holographic') computation of tree-level scattering amplitudes.
In What is the Simplest Quantum Field Theory?, with Arkani-Hamed and Cachazo, we argued that maximally supersymmetric Yang-Mills and Gravity theories share many very simple properties at tree and loop level, and we explained how non-trivial global symmetries can be understood by studying the soft limits of scattering amplitudes.
In A Duality for the S-Matrix, with Arkani-Hamed, Cachazo, and Cheung, we derived a totally new formalism for all perturbative scattering amplitudes in gauge theories, based on a contour integral over a Grassmannian manifold. In this formalism, symmetries, unitarity, and locality are all recast into a new form that is still being explored.
Effective Field Theory and Phenomenology
The force of gravity is weaker than the Electroweak forces by roughly twenty orders of magnitude, and the LHC may tell us whether new symmetries or environmental selectrion are responsible for this enormous hierarchy in scales. The LHC could also discover new stable particles that make up the universe's Dark Matter, or it could uncover something totally unexpected. I am also very interested in ideas for new experiments and new uses for existing data, as well as applications of field theory beyond the usual realm of high-energy physics.
In Discovering New Light States with Neutrino Experiments, with Essig, Harnik, and Toro, we showed how old fixed target data from Neutrino experiments could be used to discover very general low-mass, very weakly interacting new particles.
In LHC Predictions from a Tevatron Anomaly in the Top Quark Forward-Backward Asymmetry, with Bai, Hewitt, and Rizzo, we studied a particular class of seemingly well-motivated models of new physics that could have explained a Tevatron anomaly.
In Heavy Flavor Simplifed Models at the LHC, with Essig, Izaguirre, and Wacker, we studied a large class of simplified models with new heavy flavor quark partners and color octets indicative of natural new physics.
In A New Theory of Anyons, with Fitzpatrick, Kachru, Katz, and Wacker, we discovered a new 2+1 dimensional theory of anyons, and explored its properties and possible implementation in condensed matter physics.
The inhomogeneities we find in the universe today arose from the gravitational collapse of tiny primordial inhomogeneities, and these are believed to have been produced during an early epoch of inflation. In The Effective Field Theory of Inflation, with Cheung, Creminelli, Fitzpatrick, and Senatore, we derived the most general effective field theory for inflation with a single degree of freedom. The inflating cosmological background spontaneously breaks time translation invariance, and the resulting goldstone boson is the relevant mode in our effective theory. Our theory naturally computes primordial inhomogeneities, as they dominantly result from quantum fluctuations in the local time coordinate.
I will be teaching a course on Advanced Particle Physics in the fall of 2013.