Oliver Schlotterer
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Oliver Schlotterer phone: +46(0)18 471 xxxx |
RESEARCH Interests
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)
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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)
TEACHING
I plan to teach a string-theory course starting from September 2019.
Recent publications
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One-loop open-string integrals from differential equations: all-order $\alpha$'-expansions at $n$ points
2019-08-29arXiv:1908.10830
UUITP-36/19
by: Mafra, Carlos R. (Southampton U.) et al.
Abstract:
We study generating functions of moduli-space integrals at genus one that are expected to form a basis for massless $n$-point one-loop amplitudes of open superstrings and open bosonic strings. These integrals are shown to satisfy the same type of linear and homogeneous first-order differential equation w.r.t. the modular parameter $\tau$ which is known from the A-elliptic Knizhnik--Zamolodchikov--Bernard associator. The expressions for their $\tau$-derivatives take a universal form for the integration cycles in planar and non-planar one-loop open-string amplitudes. These differential equations manifest the uniformly transcendental appearance of iterated inte... -
All-order alpha'-expansion of one-loop open-string integrals
2019-08-28arXiv:1908.09848
UUITP-34/19
by: Mafra, Carlos R. (Southampton U.) et al.
Abstract:
We present a new method to evaluate the $\alpha'$-expansion of genus-one integrals over open-string punctures and unravel the structure of the elliptic multiple zeta values in its coefficients. This is done by obtaining a simple differential equation of Knizhnik-Zamolodchikov-Bernard-type satisfied by generating functions of such integrals, and solving it via Picard iteration. The initial condition involves the generating functions at the cusp $\tau\to i\infty$ and can be reduced to genus-zero integrals.... -
One-Loop String Scattering Amplitudes as Iterated Eisenstein Integrals
2019-05-20
by: Broedel, Johannes (Humboldt U., Berlin) et al.
Abstract:
In these proceedings we review and expand on the recent appearance of iterated integrals on an elliptic curve in string perturbation theory. We represent the low-energy expansion of one-loop open-string amplitudes at multiplicity four and five as iterated integrals over holomorphic Eisenstein series. The framework of elliptic multiple zeta values serves as a link between the punctured Riemann surfaces encoding string interactions and the iterated Eisenstein integrals in the final results. In the five-point setup, the treatment of kinematic poles is discussed explicitly.... -
Towards the n-point one-loop superstring amplitude. Part III. One-loop correlators and their double-copy structure
2018-12-31arXiv:1812.10971
JHEP 1908 (2019) 092
by: Mafra, Carlos R. (Southampton U.) et al.
Abstract:
In this final part of a series of three papers, we will assemble supersymmetric expressions for one-loop correlators in pure-spinor superspace that are BRST invariant, local, and single valued. A key driving force in this construction is the generalization of a so far unnoticed property at tree-level, the correlators have the symmetry structure akin to Lie polynomials. One-loop correlators up to seven points are presented in a variety of representations manifesting different subsets of their defining properties. These expressions are related via identities obeyed by the kinematic superfields and worldsheet functions spelled out in the first two part... -
Towards the n-point one-loop superstring amplitude. Part I. Pure spinors and superfield kinematics
2018-12-31arXiv:1812.10969
JHEP 1908 (2019) 090
by: Mafra, Carlos R. (Southampton U.) et al.
Abstract:
This is the first installment of a series of three papers in which we describe a method to determine higher-point correlation functions in one-loop open-superstring amplitudes from first principles. In this first part, we exploit the synergy between the co-homological features of pure-spinor superspace and the pure-spinor zero-mode integration rules of the one-loop amplitude prescription. This leads to the study of a rich variety of multiparticle superfields which are local, have covariant BRST variations, and are compatible with the particularities of the pure-spinor amplitude prescription. Several objects related to these superfields, such as thei...