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- What unifies our physical predictions?
- How does the relatively calm macroscopic universe survive and emerge from the violent quantum fluctuations of its underlying microphysics?
- How do classical notions of space and time emerge from fundamental principles, and what governs their evolution?
- How are should our classical understanding of space and time be modified to build intuition of underlying quantum reality?
- How might our current understanding of quantum mechanics need to evolve to resolve answers to the above questions?
- Double copy unification of relativistic quantum field theories.
- Double copy relevance for classical predictions in perturbative gravity.
- Predictivity question re: pointlike quantum field theories of gravity. (Are all QFT of gravity effective out of necessity?)
- Relevance of field-theory double-copy to ultra-soft properties of string theory. (See Z-theory.)
- Effective field theory of large scale structure (EFTofLSS)
- -Attractor Inflationary models.
- Discovered the color-kinematic duality in gauge theories and the associated double-copy structure of tree and multi-loop gravity theory amplitudes. Importance: Striking clarification of the intimacy between gauge and gravity theories, redundancy present in both, changing the way we calculate in and think about these theories. (For a textbook introduction can now see Anthony Zee’s Quantum Field Theory in a Nutshell, 2nd Ed., Chapter N.4. For popular science account see May 2012 cover story of Scientific American.)
with: Bern, Johansson.
- Discovered the basis (“BCJ” basis) of gauge-theory tree-level amplitudes. Importance: Led to proofs of explicit tree-level gauge-gravity amplitude-level relations (KLT) in field theory, subsequent discovery of analogous structure in string theory led to closed form string-KLT expressions and all-order expressions for string tree-amplitudes.
with: Bern, Johansson.
- Established, through explicit calculation, that the high energy behavior of maximal supergravity, contrary to popular opinion, is much better than expected – matching the known finite maximal gauge theory – through 4 loops as of now. Importance: If finite to all orders it is because of an unrecognized symmetry or mechanism whose apprehension will teach something very new about gravity.
with: Bern, Dixon, Kososwer, Roiban, Johansson.
- Established the predictive impact of certain anomalies relevant to supergravity theories, and perhaps more strikingly their underlying double-copy origins. Importance: There is mounting evidence to suggest that failure of predictivity for pure supergravity theories in four-dimensions are directly related to these anomalies, which * do not exist for supergravity theories.*
with: Kallosh, Roiban, Tseytlin.
- Established the effective field theory of cosmological large-scale structure. Importance: opens up a rigorous new way to analytically study large-scale structure taking into account the nonlinearity of small-scale perturbations with telling agreement between numerical simulations and analytic theory.
with: Foreman, Green, Hertzberg, Senatore.
- Discovered a systematic, theory-independent, approach to unitarity-based multi-loop perturbative quantization - Method of Maximal Cuts. Importance: Establishes hierarchy of relevance of -matrix information for a given theory. Trivialized unitarity state-sums for theories whose spectra are truncations of super Yang-Mills1 in 4D to just tracking glue around MHV-vertex graphs.
with: Bern, Dixon, Kosower, Roiban, Johansson.
- Established covariant prescriptions for deforming non-linear duality-invariant theories. Importance: demonstration of freedom to introduce counterterms to theories protected by duality-invariance, may be relevant to UV questions in gravity.
with: Broedel, Ferrara, Kallosh, Roiban
- Established Z-theory as the effective bi-colored scalar theory which encodes all the corrections of the open-string, and thus encodes all the ultra-soft UV behavior. Importance: Scalars theories are technically much simpler to analyze. Z-theory amplitudes offer a fascinating laboratory to study the emergence of stringy-behavior in a new and technically much simpler context.
with: Mafra and Schlotterer
So, also, theories that are orbifolds of supergravity. ↩