### Info

This seminar features recent results at the intersection of high-energy physics, string theory, and geometry and topology.

** Prerequisites:** None. Everyone is welcome. To receive announcements for
this seminar, and for the advertisement of other talks at the intersection of physics and
geometry in Heidelberg,
you may subscribe to the
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** Time and Place:** Regularly: Monday, 4 p.m.c.t., MATHEMATIKON
SR 3

Alternatively: Tuesday or Thursday, 4 p.m.c.t., various locations (or as noted below).

** Note:** As a result of the coronavirus crisis the seminar is held in fully hybrid
mode in cooperation with
JGU Mainz,
LMU Munich,
and
University of Vienna (RIND).
Please contact the organizers by e-mail to receive the link to the online seminar.

Standard time in the Winter 22/23 is Monday, 4 p.m.c.t., unless indicated otherwise.

### Schedule

Date | Speaker | Title, Abstract |
---|---|---|

October 17 | Taizan Watari (IPMU) | Towards Hodge-theoretic characterization of rational 2d SCFTs |

A 2d SCFT is obtained as the non-linear sigma model of a Ricci-flat Kahler manifold. Only special points in the moduli space of such SCFTs are rational SCFTs, where the super-chiral algebra of the SCFT is much larger than the superconformal algebra. It has been hinted 20~30 years ago by Moore and Gukov--Vafa that such special SCFTs may correspond to the target space that are characterized by a number theoretical property called "complex multiplication." We revisit the conjecture, and test and refine the conjecture statements by experimental study on examples not worked out back then. This presentation is based on a joint work ( 2205.10299 ) with Abhiram Kidambi and Masaki Okada, and also on a work in progress with M. Okada. | ||

October 24 | Albrecht Klemm (Bonn) | Feynman integrals, Calabi-Yau geometries and integrable systems |

Recently it has been realized that the parameter dependence of Feynman integrals in dimensional regularisation can be calculated explicitly using period-- and chain integrals of suitably chosen Calabi-Yau motives, where the transcendentality weight of the motive is proportional to the dimension of the Calabi Yau geometry and the loop order of the Feynman graphs. We exemplify this for the Banana graphs, the Ice Cone graphs and the Train Track graphs in two dimensions. In the latter case there is a calculational very useful relation between the differential realisation of the Yangian symmetries and the Picard-Fuchs system of compact Calabi-Yau spaces M as well as between the physical correlations functions and the quantum volume of the manifolds W that are the mirrors to M. | ||

October 31 | Lorenz Eberhardt (IAS) | Unitarity cuts of the worldsheet |

I will revisit string one-loop amplitudes in this talk. After reviewing the basics, I will explain how Witten’s \(i \epsilon\) prescription gives a manifestly convergent representation of the amplitude. I will then consider the imaginary part of the amplitude and show directly that it satisfies the standard field theory cutting rules. This leads to an exact representation of the imaginary part of the amplitude. I will also discuss physical properties of the imaginary part such as the singularity structure of the amplitude, its Regge and high energy fixed-angle behaviour and low-spin dominance. Finally, I will tease how Rademacher’s contour can be used to evaluate the full one-loop open string amplitude exactly in terms of a convergent infinite sum. | ||

November 14 | Raghu Mahajan (Stanford) | ZZ instanton amplitudes in minimal string theory at one-loop order |

We use insights from string field theory to analyze and cure the divergences in the cylinder diagram in minimal string theory, with both boundaries lying on a ZZ brane. Minimal string theory refers to the theory of two-dimensional gravity coupled to a minimal model CFT that serves as the matter sector; it includes JT gravity as a limiting case. ZZ branes are akin to D-instantons, and give rise to features that reflect the underlying discreteness of the dual theory. The exponential of the cylinder diagram represents the one-loop determinant around the instanton saddle. The finite result for this one-loop constant computed using the string field theory procedure agrees precisely with independent calculations in the dual double-scaled matrix integrals performed by several authors many years ago. | ||

November 28 | Enno Kessler (MPI Bonn) | Super Stable Maps |

J-holomorphic curves or pseudoholomorphic curves are maps from Riemann surfaces to symplectic manifolds satisfying the Cauchy-Riemann equations. J-holomorphic curves are of great interest because they allow to construct invariants of symplectic manifolds and those invariants are deeply related to topological superstring theory. A crucial step towards Gromov–Witten invariants is the compactification of the moduli space of J-holomorphic curves via stable maps which was first proposed by Kontsevich and Manin. In this talk, I want to report on a supergeometric generalization of J- holomorphic curves and stable maps where the domain is a super Riemann surface. Super Riemann surfaces have first appeared as generalizations of Riemann surfaces with anti-commutative variables in superstring theory. Super J-holomorphic curves couple the equations of classical J-holomorphic curves with a Dirac equation for spinors and are critical points of the superconformal action. The compactification of the moduli space of super J- holomorphic curves via super stable maps might, in the future, lead to a supergeometric generalization of Gromov-Witten invariants. Based on arXiv:2010.15634 [math.DG] and arXiv:1911.05607 [math.DG], joint with Artan Sheshmani and Shing-Tung Yau. | ||

December 5 | Nikita Nekrasov (Simons Center for Geometry and Physics) | Anyons hiding in gauge theory in two, three, and four dimensions |

Calogero-Moser-Sutherland system of particles is a prototypical example of a system with fractional statistics. I review the old and new connections of this system to (super) Yang-Mills theory in various dimensions. | ||

December 12 | Ida Zadeh (Uni Mainz) | Heterotic Strings on \(T^3/\mathbb{Z}_2\), Nikulin involutions and M-theory |

I will discuss compactification of the heterotic string on the smooth, flat 3-manifold \(T^3/\mathbb{Z}_2\), without supersymmetry. The low energy dynamics of the corresponding ten dimensional heterotic supergravity will be described. The semi-classical theory has both Coulomb and Higgs branches of non-supersymmetric vacua. An exact worldsheet description of the compactification will then be presented using the framework of asymmetric orbifolds of \(T^3\), where the orbifold generator involves a Nikulin non-symplectic involution of the even self-dual lattice of signature \((19,3)\). This construction gives a novel conformal field theory description of the semi-classical field theory moduli space and reveals a rich pattern of transitions amongst Higgs and Coulomb branches. | ||

December 19 | Ralph Blumenhagen - Niccolò Cribiori (LMU Munich) | Cobordism, K-theory and tadpoles |

The absence of global symmetries is widely believed to be a principle of quantum gravity. Recently, it has been generalised to the statement that the cobordism group of quantum gravity must be trivial. Indeed, a non-trivial group detects a higher-form global symmetry, which has then to either be gauged or broken. In the case in which it is broken, defects have to be introduced into the setup. These can be end-of-the-world branes furnishing a dynamical realization of cobordism, of which we will provide a new concrete example. In the case in which the symmetry is gauged, we will argue that there is a non-trivial interplay between cobordism and K-theory, leading to the construction of type IIB/F-theory tadpoles from a bottom-up perspective. This interpretation of cobordism and K-theory as charges in quantum gravity can be given further support when passing from groups of the point to groups of a generic manifold \(X\). We will argue that these more general groups have a natural interpretation in terms of the dimensional reduction of the theory on \(X\). A systematic analysis can possibly lead to the prediction of new contributions to string theory tadpoles. | ||

January 9 | Nicolo Piazzalunga (Rutgers) | The Index of M-Theory |

I'll introduce the higher-rank Donaldson-Thomas theory for toric Calabi-Yau three-folds, within the setting of equivariant K-theory. I'll present a factorization conjecture motivated by Physics. As a byproduct, I'll discuss some novel properties of equivariant volumes, as well as their generalizations to genus-zero Gromov-Witten theory of non-compact toric varieties. | ||

January 30 | Konstantin Wernli (Southern Denmark) | On Globalization of Perturbative Partition Functions in the Batalin-Vilkovisky formalism |

In the Batalin-Vilkovisky (BV) formalism, one can define a perturbative (i.e. given by Feynman graphs and rules) partition function \(Z(x_0)\) for any choice of classical background (solution to Euler-Lagrange (EL) equations) \(x_0\). In some examples one can extract from \(Z\) a volume form on the smooth part of the moduli space of solutions to EL equations, and compare its integral with non-perturbative approaches to quantization. I will review this construction, some results from examples in the literature and ongoing joint work with P. Mnev about the behaviour at singular points \(x_0\). | ||

Feburary 6 | Renann Lipinski Jusinskas | Asymmetrically twisted strings |

In this talk I will present a worldsheet model obtained from "twisting" the target space CFT of conventional string theory. The physical spectrum becomes finite and corresponds to the massless spectrum of closed strings plus a single massive level of the open string. The underlying idea is to explore the field/string theory interface in both directions. On one hand, the goal is to generate effective field theories describing massive higher spins using worldsheet methods. Conversely, we may try to use field theory methods to obtain a systematic description of string scattering amplitudes using field theory methods. | ||

February 13 | N.N. | T.B.A. |

Abstract forthcoming |

### Organizers

Prof. J. Walcher, walcher@uni-heidelberg.de

Dr. Simone Noja,
noja@mathi.uni-heidelberg.de