Titles and abstracts as pdf.
Links to recording and slides of talks can be found below the corresponding abstract.
Abstract: In the simplest case of the quantized electromagnetic field confined between two perfectly conducting plates, the set-up of the Casimir effect, the additional topological degrees of freedom that give rise to contributions to the partition function that scale with the area of the plates are identified.
Slides: pdf
Video: Link
Abstract: AKSZ construction suggests some glimpses of an original point of view of the interplay between gauge symmetry and supersymmetry.Indeed, several examples of topological twist of supersymmetric field theories can be described in the AKSZ formalism. The equivariant extension of these theories can be easily em bedded in the AKSZ construction. I will describe how to extend the BV formalism in order to deal with the equivariant extension of the classical master equation.
Slides: pdf
Video: Link
Abstract: A prominent example of the BV-BFV formalism is the Poisson Sigma Model (PSM), a 2-dimensional topological field theory. In this "teaser talk" we will introduce PSM as an AKSZ theory and we will report joint work with Nicolas Martinez Alba (arXiv:1912.07697) on the integration of Poly-Poisson structures via PSM, and joint work in progress with Rui Fernandes (based on arXiv:1805.12043 ) regarding PSM and genus integration.
Video: Link
Abstract: Usual BV formalism for local gauge field theories is defined in terms of suitable jet-bundles. At the level of equations of motion this can be extended to more general supermanifolds by representing a gauge theory as a (generalized) AKSZ type sigma model using so-called parent formulation. This naturally leads to a concept of gauge PDE which is a main subject of the talk. In this approach the Lagrangian is encoded in the compatible graded presymplectic structure and can be recovered as a presymplectic version of the AKSZ action, giving a supergeometrical interpretation of the familiar frame-like Lagrangians. Existing and potential applications to higher-spin gauge theories and holographic dualities are briefly discussed.
Slides: pdf
Video: Link
Abstract: 1. Those who love BV think that BV is a language, and all interesting statements may be turned into a statement that some action solves master equation and all constructions are some kinds of BV integral. In BV language the statement that function on a manifold (action) is invariant under the action of certain Lie algebra is just a statement that the extended action (involving ghosts) solves classical master equation. However, this form of the action is not invariant under the BV integral, so we should generalise. Thus, we get the notion of infinity-representation of the Lie algebra, where zeroth power of the Lie algebra is mapped to a function on a manifold (invariant action), k-th power - to k-polyvector fields, that satisfy some quadratic equations. If bivector part of this map is nonzero, the infinity-representation is no longer representation, rather it is what is called (in physics literature) "the action of the Lie algebra that closes on-shell", and I would like to add "completed by bivectors". I will describe appearance of such infinity-representation of $so(n)$ acting on R^m, m<n, using BV integral. Why do I think it is interesting? Mostly, because higher supersymmetries "close on-shell".
2. In the second part of the talk I will recall the "pure spinor construction" that could be given the following meaning. The maximal matter supersymmetric field theory N=1 D=10 SYM (where SUSY is "closed on-shell") is obtained by induction of operations to cohomology from the theory of the BF-type (supercommutative DGA with values in End(V), i.e. matrices) followed by Z_2 projection. Actually, this DGA is a bicomplex rather than complex with differential D=D_1+D_2, and we induce operations to cohomology of D_1 that turned to be fields and gauge symmetries of N=1 D=10 SYM together with antifields, i.e. they are "doubled". In other terms, we obtained a homological vector field together with the BV form. So we can pass from the BV theory on T*M with the action given by a vector field, to BV theory on M with the action given by the Hamiltonian of the vector field. Such procedure is familiar if one wants to pass from BF theory to CS theory in D=3. For brevity I will call it Z_2 projection.
3. Supersymmetry is an obvious standard global symmetry of original BF theory, while under induction (and further Z_2 projection) it turns into infinity-representation. I will show an explicite formula for bivector, and put as an open problem to find such bivectors in other theories with higher supersymmetries (in particular, in N=2 D=4, probably using harmonic superspaces approach) and also in various supergravity theories, including the "M-theory" D=11 N=1.
Based on old but not well known papers arXiv:0705.2191 "On Pure Spinor Superfield Formalism" JHEP 0710:074,2007 and arXiv:0707.1906 "Materializing Superghosts" JETP Lett.86:439-443,2007 by Victor Alexandrov, Dmitry Krotov, Andrei Losev, Vyacheslav Lysov
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Abstract: The Gaudin model is an integrable system associated to a Lie algebra and a finite collection of points in the complex plane. We report on work in progress, joint with Owen Gwilliam and Brian Williams, which aims to recover this integrable system by studying a gauge theory (the so-called "mixed BF theory") in three-dimensional Euclidean space coupled to a number of line defects.
Slides: pdf
Video: Link
Abstract: It is well known that the moduli space of flat $\mathfrak g$-connections comes with a Poisson structure, provided the Lie algebra $\mathfrak g$ is equipped with an invariant pairing. In a joint work with Anton Alekseev, Florian Naef and Pavol Severa, we show that if $\mathfrak g$ is a Lie superalgebra with an odd,invariant pairing, then the moduli space has a natural Batalin-Vilkovisky structure. Moreover, for the queer Lie superalgebra, this BV structure contains the BV structure coming from the Goldman-Turaev Lie bialgebra, giving an interpretation of the Turaev cobracket in terms of flat connections.
Slides: pdf
Video: Link
Abstract: In this talk I will present the results of the recent paper by Michele Schiavina and myself, where we discuss how the BV-BFV framework can be applied to long-range degrees of freedom in theories like QED and the massless scalar field. By using the systematic BV-BFV approach we resolve some of the controversies present in the literature, related to the interpretation and the status of "large gauge transformations".
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Abstract: I will describe a toy model for a BV action for string field theory by considering equivalence classes of degree one elemnts in a graded Lie super algebra and, in particular, Maurer Cartan elements. Depending on the amount of world/line supersymmetry we then recover kown theories, such as Yang Mills theory and the bosonic sector of Type II Supergravity.
Slides: pdf
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Abstract: I will discuss a field-theoretic interpretation of Ruelle zeta function, which "counts" prime geodesics on hyperbolic manifolds, as the partition function for BF theory with an unusual gauge fixing condition. This suggests a rephrasing of a conjecture due to Fried, on the equivalence between Ruelle zeta function and analytic torsion, as gauge fixing independence in the BV formalism.
Slides: pdf
Video: Link