My research is centered on the rich interplay between string theories, unifying structures in perturbative field theories and modern topics in number theory. More specifically, I am studying scattering amplitudes in string and field theories as a smoking gun for striking connections between gauge theories, gravity and effective field theories. This includes interdisciplinary research on the intriguing mathematical structures of multiple zeta values, polylogarithms and their generalizations to higher genus which arise in both string amplitudes and Feynman integrals. My work has pinpointed string-theory origins of double-copy structures in perturbative gravity, a variety of surprising field-theory structures in string amplitudes and the first instances of elliptic multiple zeta values in physics.
ERC-StG project UNISCAMP – The unity of scattering amplitudes: gauge theory, gravity, strings and number theory
Scattering amplitudes are central observables in quantum field theory and provide essential information about the quantum consistency of perturbative gravity. Precise control of the physical and mathematical properties of scattering amplitudes holds the key to long-standing questions on fundamental interactions and the structure of space and time. As a concrete leap in this direction, UNISCAMP addresses predictions in gauge theories, gravity and effective theories through
- the efficient computation and compact representation of scattering amplitudes and,
- decoding their hidden structures & symmetries and their rich web of connections.
String-theory methods will complement conventional approaches to scattering amplitudes, and UNISCAMP will combine the insights from
- the point-particle limit of superstrings & heterotic strings and,
- the recent ambitwistor strings which directly compute field-theory amplitudes.
Both of them naturally incorporate the double-copy relation between gauge-theory & gravity amplitudes and extend the framework to effective field theories describing pions and other low-energy states. It is a primary goal of UNISCAMP to pinpoint the unifying principles connecting a wide range of field and string theories.
Moreover, field- and string-theory amplitudes exhibit an intriguing mathematical structure: Their Feynman- and moduli-space integrals yield special functions such as polylogarithms which became a vibrant common theme of high-energy physics and number theory. An interdisciplinary goal of UNISCAMP is to
- investigate the low-energy expansion of multiloop string amplitudes and,
- extract an organizing scheme for iterated integrals on higher-genus Riemann surfaces.
Review material that you cannot find on the arXiv
- The number theory of string amplitudes (draft version of a proceedings article for the conference “Numbers and Physics”, ICMAT, Madrid, Spain, September 2014)
- One-loop string scattering amplitudes as iterated Eisenstein integrals jointly written with Johannes Broedel (draft version of a proceedings article for the KMPB Conference “Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory”, DESY Zeuthen, Zeuthen, Germany, October 2017)
I am teaching a doublet of master courses on string theory from fall 2022 to spring 2023, the lecture notes including homework problems can be found in the following pdf.
Moreover, you can find the notes of Max Guillen's extra lectures on “Advanced Topics in String Theory” in the following pdf.