### 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
Mailing List.

** 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 21 | N.N. | T.B.A. |

This is the abstract | ||

November 28 | N.N. | T.B.A. |

Abstract forthcoming | ||

December 5 | N.N. | T.B.A. |

This is the abstract | ||

December 12 | N.N. | T.B.A. |

Abstract forthcoming | ||

December 19 | N.N. | T.B.A. |

This is the abstract | ||

January 9 | N.N. | T.B.A. |

Abstract forthcoming | ||

January 16 | N.N. | T.B.A. |

This is the abstract | ||

January 23 | N.N. | T.B.A. |

Abstract forthcoming |

### Organizers

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

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