Oliver Schlotterer

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 stringtheory origins of doublecopy structures in perturbative gravity, a variety of surprising fieldtheory structures in string amplitudes and the first instances of elliptic multiple zeta values in physics.
ERCStG 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 longstanding 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.
Stringtheory methods will complement conventional approaches to scattering amplitudes, and UNISCAMP will combine the insights from
 the pointparticle limit of superstrings & heterotic strings and,
 the recent ambitwistor strings which directly compute fieldtheory amplitudes.
Both of them naturally incorporate the doublecopy relation between gaugetheory & gravity amplitudes and extend the framework to effective field theories describing pions and other lowenergy 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 stringtheory amplitudes exhibit an intriguing mathematical structure: Their Feynman and modulispace integrals yield special functions such as polylogarithms which became a vibrant common theme of highenergy physics and number theory. An interdisciplinary goal of UNISCAMP is to
 investigate the lowenergy expansion of multiloop string amplitudes and,
 extract an organizing scheme for iterated integrals on highergenus 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)

Oneloop 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 stringtheory course starting from September 2019.
Recent publications

Allorder differential equations for oneloop closedstring integrals and modular graph forms
20191112arXiv:1911.03476
by: Gerken, Jan E.
Abstract:
We investigate generating functions for the integrals over worldsheet tori appearing in closedstring oneloop amplitudes of bosonic, heterotic and typeII theories. These closedstring integrals are shown to obey homogeneous and linear differential equations in the modular parameter of the torus. We spell out the firstorder CauchyRiemann and secondorder Laplace equations for the generating functions for any number of external states. The lowenergy expansion of such torus integrals introduces infinite families of nonholomorphic modular forms known as modular graph forms. Our results generate homogeneous first and secondorder differential equations for arbitrary such modular graph forms and can be v... 
Oneloop openstring integrals from differential equations: allorder $\alpha$'expansions at $n$ points
20190829arXiv:1908.10830
UUITP36/19
by: Mafra, Carlos R. (Southampton U.) et al.
Abstract:
We study generating functions of modulispace integrals at genus one that are expected to form a basis for massless $n$point oneloop amplitudes of open superstrings and open bosonic strings. These integrals are shown to satisfy the same type of linear and homogeneous firstorder differential equation w.r.t. the modular parameter $\tau$ which is known from the Aelliptic KnizhnikZamolodchikovBernard associator. The expressions for their $\tau$derivatives take a universal form for the integration cycles in planar and nonplanar oneloop openstring amplitudes. These differential equations manifest the uniformly transcendental appearance of iterated inte... 
Allorder alpha'expansion of oneloop openstring integrals
20190828arXiv:1908.09848
UUITP34/19
by: Mafra, Carlos R. (Southampton U.) et al.
Abstract:
We present a new method to evaluate the $\alpha'$expansion of genusone integrals over openstring punctures and unravel the structure of the elliptic multiple zeta values in its coefficients. This is done by obtaining a simple differential equation of KnizhnikZamolodchikovBernardtype 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 genuszero integrals.... 
OneLoop String Scattering Amplitudes as Iterated Eisenstein Integrals
20190520
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 lowenergy expansion of oneloop openstring 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 fivepoint setup, the treatment of kinematic poles is discussed explicitly.... 
Towards the npoint oneloop superstring amplitude. Part III. Oneloop correlators and their doublecopy structure
20181231arXiv: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 oneloop correlators in purespinor 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 treelevel, the correlators have the symmetry structure akin to Lie polynomials. Oneloop 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...