<\/p>\n
Vladislav Kupriyanov<\/strong> (UFABC, Sao Paulo) |\u00a0Poisson Electrodynamics<\/strong><\/em> | 17 March 2025<\/p>\n Poisson electrodynamics is the semi-classical limit of noncommutative U(1) gauge theory. In this approximation, the noncommutativity of space coordinates is described by a Poisson bracket. In this talk I will describe the construction of Poisson gauge algebra using techniques based on symplectic embeddings of Poisson structures. We also construct the gauge covariant Poisson field strength and gauge invariant action, from which we derive Maxwell-Poisson equations. We provide a geometric construction of a gauge invariant action functional which minimally couples a dynamical charged particle to a background electromagnetic field. Our constructions are elucidated by several explicit examples.<\/p>\n <\/p>\n Si Li<\/strong>\u00a0(Tsinghua U., Beijing) | Quantum Mechanics with zero Hamiltonian<\/strong><\/em> | 19 February 2025<\/p>\n Every kid learns how to deal with Hamiltonian operators in quantum mechanics. One might think the theory would be boring if the Hamiltonian is zero. However, I will explain it is not trivial but in fact has rich structures and deep connections with non-commutative geometry.<\/p>\n <\/p>\n Carlo Iazeolla<\/strong> (Guglielmo Marconi U., Roma) | Fractional spins, unfolding and holography: a parent theory for dual higher spin gravities<\/strong><\/em> | 10 February 2025<\/p>\n I will show how Vasiliev\u2019s 4D higher-spin gravity and 3D colored conformal higher-spin gravity (i.e., colored conformal matter fields coupled to conformal higher-spin gauge fields and color gauge fields) emerge as two consistent reductions of a common parent model. The latter consists, on-shell, of a flat superconnection valued in a fractional-spin extension of Vasiliev\u2019s higher-spin algebra. The higher-spin gravity and colored conformal higher-spin gravity reductions are characterised by dual structure groups, and their embedding in a common parent model provides a rationale for deriving holographic relations between them.<\/p>\n <\/p>\n Patricio Salgado-Rebolledo<\/strong> (U. Adolfo Ibanez, Santiago) | Maxwell gravity from an expansion in the cosmological constant<\/em><\/strong> | 22 January 2025<\/p>\n In this talk, I will construct an expansion of (A)dS gravitational theories in powers of the cosmological constant, in complete analogy to expansions of gravity in powers of the (inverse) speed of light previously considered in the literature. Using this result, I will show that the Maxwell gravity theory proposed by de Azc\u00e1rraga, Kamimura and Lukierski appears as the subleading term in the small-cosmological-constant expansion of (A)dS Einstein gravity. In the three-dimensional case, the expansion produces Chern-Simons theories invariant under Maxwell-like extensions of the Poincar\u00e9 symmetry. The subleading term corresponds to Maxwell-invariant Chern-Simons gravity, which has been previously shown to admit an asymptotic symmetry given by an extended BMS algebra. I will focus on this example and reduce the theory to the boundary to find its two-dimensional classical dual field theory and show how such a theory can be related to a cosmological constant expansion of Liouville theory. Finally, I will elaborate on possible extensions and future directions.<\/p>\n <\/p>\n Keith Glennon<\/strong> (OIST, Okinawa) |\u00a0K27 Symmetry of String Theory and Bosonic M-Theory<\/strong><\/em> | 13 January 2025<\/p>\n We will show that the dynamics encoded in the non-linear realisation of the semi-direct product of the very extended Lorentzian Kac-Moody algebra K27 with its vector representation contains the low energy effective action of the closed bosonic string. We will then discuss implications of this result regarding ‘bosonic M-theory’.<\/p>\n <\/p>\n Giorgio Leone<\/strong> (SNS Pisa) |\u00a0New non-supersymmetric tachyon-free orientifolds in 6d and unitarity constraints<\/em><\/strong> | 18 December 2024<\/p>\n The absence of supersymmetry is often accompanied by instabilities emerging from tadpoles or tachyons in the spectrum. While tadpoles are ubiquitous in any non-supersymmetric set-up, few models are known to be tachyon-free. In this seminar, I will focus on orientifold constructions in lower dimensions which do not have tachyons and enjoy Brane Supersymmetry Breaking (BSB). These vacua are characterised by a simultaneous presence of a tree-level supersymmetric closed string sector coupled with a non-supersymmetric open string one, which underlies a non-linear realisation of supersymmetry. After reviewing the original construction in six dimensions built on the T^4<\/sup>\/Z_2 orbifold, I will present an almost rigid variation that can only be deformed via overall brane recombination. Afterwards, I will describe the BSB orientifold built upon the T^4<\/sup>\/Z_4 orbifold which, in contrast to the previous case, does not admit any continuous deformation, leaving only space for a discrete one encoded into a non-vanishing Kalb-Ramond field. Finally, I will comment on the unitarity constraints arising from 2d defects coupled to the R-R 2-forms required by the Green-Schwarz-Sagnotti mechanism.<\/p>\n <\/p>\n Alessandro Tomasiello<\/strong> (U. Milano Bicocca) | Higher spins and Finsler geometry<\/strong><\/em> | 3 December 2024<\/p>\n Finsler geometry is a natural generalization of (pseudo-)Riemannian geometry, where the line element is not the square root of a quadratic form but a more general homogeneous function. Parameterizing this in terms of symmetric tensors suggests a possible interpretation in terms of higher-spin fields. We will see here that, at linear level in these fields, the Finsler version of the Ricci tensor leads to the curved-space Fronsdal equation for all spins, plus a Stueckelberg-like coupling. Nonlinear terms can also be systematically analyzed, suggesting a possible interacting structure. No particular choice of spacetime dimension is needed. The Stueckelberg mechanism breaks gauge transformations to a redundancy that does not change the geometry. This creates a serious issue: non-transverse modes are not eliminated, at least for the versions of Finsler dynamics examined in this paper.<\/p>\n <\/p>\n Guillaume Bossard<\/strong> (CPHT, Palaiseau) | Higher dual fields and E11<\/strong><\/em> | 26 November 2024<\/p>\n We construct a pseudo-Lagrangian that is invariant under rigid E<\/span>11<\/span><\/span><\/span><\/span><\/span><\/span><\/span> and transforms as a density under E<\/span>11<\/span><\/span><\/span><\/span><\/span><\/span><\/span> generalised diffeomorphisms. The gauge-invariance requires the use of a section condition studied in previous work on E<\/span>11<\/span><\/span><\/span><\/span><\/span><\/span><\/span> exceptional field theory and the inclusion of constrained fields that transform in an indecomposable E<\/span>11<\/span><\/span><\/span><\/span><\/span><\/span><\/span>-representation together with the E<\/span>11<\/span><\/span><\/span><\/span><\/span><\/span><\/span> coset fields. We show that, in combination with gauge-invariant and E<\/span>11<\/span><\/span><\/span><\/span><\/span><\/span><\/span>-invariant duality equations, this pseudo-Lagrangian reduces to the bosonic sector of non-linear eleven-dimensional supergravity for one choice of solution to the section condition. For another choice, we reobtain the E<\/span>8<\/span><\/span><\/span><\/span><\/span> exceptional field theory and conjecture that our pseudo-Lagrangian and duality equations produce all exceptional field theories with maximal supersymmetry in any dimension. We also describe how the theory entails non-linear equations for higher dual fields, including the dual graviton in eleven dimensions. Furthermore, we speculate on the relation to the E<\/span>10<\/span><\/span><\/span><\/span><\/span><\/span><\/span> sigma model.<\/p>\n <\/p>\n Saurabh Pant<\/strong> (IISER, Pune) |\u00a0Supersymmetric Yang-Mills theories without anti-commuting variables<\/strong><\/em> | 20 November 2024<\/p>\n In this talk, my main focus will be formulating supersymmetric Yang-Mills theories without anti-commuting variables, thus characterizing them as purely bosonic theories. I will discuss the existence of the transformation (Nicolai map) of the bosonic fields such that the Jacobian determinant of the transformation exactly cancels against the product of the fermion and ghost determinants in critical dimensions where supersymmetric Yang-Mills theories exist. I will discuss various aspects of the map, like gauge dependency and uniqueness, and describe its applications to physics – specifically to scattering amplitudes and correlation functions.<\/p>\n <\/p>\n Maximo Banados<\/strong> (Pontificia Universidad Cat\u00f3lica de Chile, Santiago) |\u00a0Weyl symmetry and symmetry breaking<\/strong><\/em> | 15 November 2024<\/p>\n We present a Weyl invariant equation for Gravity by gauging the global Weyl invariance of vacuum Einstein equations. The equation is linear in the curvature and a natural generalization of Einstein equations to Weyl geometry. The system has 5 physical polarizations, two tensor modes, two vectors modes and one scalar, associated to the cosmological constant. An exact black hole solution is found and we discuss the dynamics on Friedman backgrounds and the evolution of cosmological perturbations.<\/p>\n <\/p>\n Kristiansen Lara<\/strong> (CECs, Valdivia) |\u00a0Hagedorn Behavior and Log Corrections to Geometrized Integrable Systems<\/strong><\/em> | 11 October 2024<\/p>\n The seminal work of Brown and Henneaux [1] initiated the exploration of the various asymptotic faces of three-dimensional General Relativity (GR). One of these, discovered by P\u00e9rez, Tempo, and Troncoso, is the duality between integrable systems and AdS$_3$ GR [2]. Specifically, they show that under suitable boundary conditions, along with a specific asymptotic behavior of the Lagrange multipliers, Einstein’s equations reduce to (two independent copies of) the Korteweg-de Vries (KdV) equation. In this talk, we show that under the same boundary conditions but with a different asymptotic behavior, a different integrable hierarchy emerges, known as the Dym hierarchy, whose gravitational configuration corresponds to a black hole whose properties differs from its KdV counterpart: It exhibit constant Hawking temperature (Hagedorn behavior), and therefore, a vanishing angular momentum chemical potential and inverse heat capacity, seemingly leaving no room for thermal fluctuations\u2014i.e., no log corrections to the Bekenstein-Hawking entropy. Following the change of ensemble approach of [3], we address this problem and compute its log corrections. Conclusions and further prospects are discussed.<\/p>\n [1] Brown, Henneaux, Commun. Math. Phys. 104 (1986) 207-226. <\/p>\n <\/p>\n <\/p>\n Viacheslav Krivorol<\/strong> (ITMP MSU, Steklov Mathematical Institute) |\u00a0First-order GLSM construction in sigma models: complex projective spaces and beyond<\/b><\/em> | 5 September 2024<\/p>\n Sigma models form a class of field theories that play a crucial role in various branches of modern theoretical and mathematical physics. However, studying these models is challenging due to the highly nonlinear nature of their Lagrangians. There are some specific methods, such as the background field method, that can be used to study these models, but they have some limitations.<\/p>\n There is an alternative recently proposed method, called \u00ab\u00a0the first-order GLSM formulation\u00a0\u00bb (or \u00ab\u00a0Gross-Neveu formalism\u00a0\u00bb), for studying sigma models. In this method one cast these models as gauge theories with a finite number of interactions using the idea of symplectic reduction. Instead of presenting general results, however, I will illustrate the ideas using the simplest example, the CP^n sigma model. I will then explain how these ideas can be extended to other target spaces.<\/p>\n Based on joint works with Dmitri Bykov: https:\/\/arxiv.org\/abs\/2306.04555<\/a>, https:\/\/arxiv.org\/abs\/2407.20423<\/a><\/p>\n <\/p>\n Subho Chatterjee<\/strong> (UC Davis) |\u00a0Probabilities and Supergeometry: Measurement theory for dynamical discrete systems<\/strong><\/em> | 16 July 2024<\/p>\n Discrete probabilistic systems, like bits on a computer or faces of a coin, abound in nature. We propose a geometric model describing dynamics and measurement theory for such systems. Our approach is covariant with respect to choices of clocks and laboratories. The configuration space is a super phasespacetime modelled by an odd dimensional symplectic supermanifold, observables are superfunctions and states are suitable (star) squares of superfunctions. The data of an odd dimensional symplectic supermanifold canonically incorporates dynamics. We also obtain dynamical probabilities using convex polyhedral cones and find that they obey Markov-like evolution.<\/p>\n <\/p>\n
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\n[2] P\u00e9rez, Tempo, and Troncoso, 1605.04490.
\n[3] Pathak, Porfyriadis, Strominger, Varela, 1612.04833; Grumiller, P\u00e9rez, Tempo, Troncoso, 1705.1060.<\/p>\nAcademic year 2023-2024<\/h5>\n
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