5-9. Sep 2023
Speakers
Mon 10:30 Cederwall, 16:00 Arvanitakis
Tue 10:30 Roytenberg, 16:00 Schupp
Wed 10:30 Hull, 16:00 Strobl
Thur 10:30 Szabo, 16:00 Grigoriev Friday postdocs/students
Organizers: A. Chatzistavrakidis, L. Jonke, J. Rossell
Present also: P. Dominis Prester, Marija Dimitrijević Ćirić, Z. Škoda
To get some feeling of the subject enjoyed by the participants, we list some of their (recent or relevant) papers or talks
The pure spinor superfield formalism reveals that, in any dimension and with any amount of supersymmetry, one particular supermultiplet is distinguished from all others. This “canonical supermultiplet” is equipped with an additional structure that is not apparent in any component-field formalism: a (homotopy) commutative algebra structure on the space of fields. The structure is physically relevant in several ways; it is responsible for the interactions in ten-dimensional super Yang-Mills theory, as well as crucial to any first-quantised interpretation. We study the L∞ algebra structure that is Koszul dual to this commutative algebra, both in general and in numerous examples, and prove that it is equivalent to the subalgebra of the Koszul dual to functions on the space of generalised pure spinors in internal degree greater than or equal to three. In many examples, the latter is the positive part of a Borcherds-Kac-Moody superalgebra. Using this result, we can interpret the canonical multiplet as the homotopy fiber of the map from generalised pure spinor space to its derived replacement. This generalises and extends work of Movshev-Schwarz and Gálvez-Gorbounov-Shaikh-Tonks in the same spirit. We also comment on some issues with physical interpretations of the canonical multiplet, which are illustrated by an example related to the complex Cayley plane, and on possible extensions of our construction, which appear relevant in an example with symmetry type .
Martin Cederwall, Jakob Palmkvist, -algebras for extended geometry from Borcherds superalgebras, Commun. Math. Phys. 369, 721-760 (2019) doi
Alex S. Arvanitakis, Topological defects as [lagrangian correspondences], Phys. Rev. D 107, 066016, 2023 arXiv:2301.04143 doi
Topological defects attract much recent interest in high-energy and condensed matter physics because they encode (non-invertible) symmetries and dualities. We study codimension-1 topological defects from a hamiltonian point of view, with the defect location playing the role of `time'. We show that the Weinstein symplectic category governs topological defects and their fusion: each defect is a lagrangian correspondence, and defect fusion is their geometric composition. We illustrate the utility of these ideas by constructing S- and T-duality defects in string theory, including a novel topology-changing non-abelian T-duality defect.
We introduce a technique to realise brane wrapping and double dimensional reduction in the context of AKSZ topological sigma models and also in their target spaces, which are symplectic Ln-algebroids (i.e. QP-manifolds). Our procedure involves a novel coisotropic reduction combined with an AKSZ transgression that realises degree-shifting; the reduced QP-manifold depends on topological data of the `wrapped' cycle. We check our procedure against the known rules for fluxes under wrapping in the context of M-theory/type IIA duality, and we also find a new relation between Courant algebroids and Poisson manifolds.
Dmitry Roytenberg, AKSZ-BV formalism and Courant algebroid-induced topological field theories, Lett. Math. Phys. 79, 143-159 (2007) doi hep-th/0608150
Athanasios Chatzistavrakidis, Larisa Jonke, Thomas Strobl, Grgur Šimunić, Topological Dirac sigma models and the classical master equation, J. Physics A 56:1 015402 doi
Athanasios Chatzistavrakidis, Larisa Jonke, Basic curvature and the Atiyah cocycle in gauge theory, arXiv:2302.04956
Athanasios Chatzistavrakidis, Georgios Karagiannis, Peter Schupp, Graded geometry and tensor gauge theories, arXiv:2004.10730
P. Schaller, T. Strobl, Poisson structure induced (topological) field theories, Modern Phys. Lett. A 9 (1994), no. 33, 3129–3136, doi; Introduction to Poisson -models, Low-dimensional models in statistical physics and quantum field theory (Schladming, 1995), 321–333, Lecture Notes in Phys. 469, Springer 1996.
Thomas Strobl, Gravity from Lie algebroid morphisms, Comm. Math. Phys. 246 (2004), no. 3, 475–502, Algebroid Yang-Mills theories, Phys. Rev. Lett. 93 (2004), no. 21, 211601, 4 pp. doi
M. Bojowald, A. Kotov, T. Strobl, Lie algebroid morphisms, Poisson sigma models, and off-shell closed gauge symmetries, J. Geom. Phys. 54 (2005), no. 4, 400–426, doi
Ctirad Klimčik, T. Strobl, WZW-Poisson manifolds, J. Geom. Phys. 43 (2002), no. 4, 341–344, doi
Dionysios Mylonas, Peter Schupp, Richard J. Szabo, Nonassociative geometry and twist deformations in non-geometric string theory, arXiv:1402.7306; Membrane sigma-models and quantization of non-geometric flux backgrounds, JHEP 1209 (2012) 012; Non-geometric fluxes, quasi-Hopf twist deformations and nonassociative quantum mechanics, J. Math. Phys. 55, 122301 (2014)
L. Müller, R. J. Szabo, L. Szegedy, Symmetry defects and orbifolds of two-dimensional Yang–Mills theory, Lett. Math. Phys. 112, 18 (2022) doi
Alex S. Arvanitakis, Olaf Hohm, Chris Hull, Victor Lekeu, Homotopy transfer and effective field theory I: tree-level, Fortschritte der Physik 70:2-3 (2022) 2200003 doi
We use the dictionary between general field theories and strongly homotopy algebras to provide an algebraic formulation of the procedure of integrating out of degrees of freedom in terms of homotopy transfer. This includes more general effective theories in which some massive modes are kept while other modes of a comparable mass scale are integrated out, as first explored by Sen in the context of closed string field theory. We treat -algebras both in terms of a nilpotent coderivation and, on the dual space, in terms of a nilpotent derivation (corresponding to the BRST charge of the field theory) and provide explicit formulas for homotopy transfer. These are then shown to govern the integrating out of degrees of freedom at tree level, while the generalization to loop level will be explored in a sequel to this paper.
Created on June 2, 2023 at 11:47:20. See the history of this page for a list of all contributions to it.