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**Time: ** 23. December 2022, 11:00h

**Place: ** Faculty of Physics, room 665

**Speaker: ** Marko Vojinovic

**Title: ** Introduction to category theory and n-groups (part 2)

**Abstract:**

This is the second of a sequence of lectures about higher category theory and n-groups. We will introduce the notions of a category, a group, and a functor, after which we shall give a couple of examples convenient for physics. If time permits, we will also introduce the notions of a strict and weak 2-category, a 2-group, and a crossed module, also with appropriate examples.

The lecture is based on material from papers arXiv:q-alg/9705009, arXiv:1003.4485.

**Time: ** 16. December 2022, 11:00h

**Place: ** Faculty of Physics, room 665, and online

**Speaker: ** Marko Vojinovic

**Title: ** Introduction to category theory and n-groups

**Abstract:**

This is the first of a sequence of lectures about higher category theory and n-groups. We will discuss the motivation for introducing n-groups, and demonstrate some of their basic properties. After introducing the idea of higher groups and discussing why they should be relevant for physics, we will demonstrate the equivalence between a strict 2-group and a crossed module, which is a technically more convenient tool. We will also discuss everything on the example of the Poincaré 2-group, which should help us to build some intuition.

The lecture is motivated mainly by papers arXiv:q-alg/9705009, arXiv:1003.4485.

**Time: ** 7. October 2022, 11:00h

**Place: ** Faculty of Physics, room 665, and online

**Speaker: ** Pavle Stipsic

**Title: ** Exponential Corrections to Black Hole Entropy

**Abstract:**

We will give an overview of the results of the paper by A. Chatterjee and A. Ghosh, *Phys. Rev. Lett.* **125**, 041302 (2020).

**Time: ** 9. September 2022, 11:00h

**Place: ** Institute of Physics, room "Dragan Popovic", and online

**Speaker: ** Tatjana Vukasinac

**Title: ** Hamiltonian analysis of general relativity in first order formalism (in self-dual variables) in the presence of a weakly isolated horizon

**Abstract:**

We perform a canonical analysis of general relativity in first order formalism (in self-dual variables), for spacetimes with a weakly isolated horizon (WIH) as an internal boundary. Isolated horizons are quasilocal generalizations of event horizons and their definition is purely geometrical. On the other hand, the covariant action and the Hamiltonian formulation of the theory are sensitive to the choices of variables and boundary terms. We show that the choice of dynamical variables on WIH is not unique and use this freedom to construct different consistent canonical formulations.

**Time: ** 10. June 2022, 11:00h

**Place: ** Faculty of Physics, room 665, and online

**Speaker: ** Maja Buric

**Title: ** Fuzzy BTZ

**Abstract:**

We introduce recently proposed fuzzy version of the BTZ black hole and discuss some of its physical properties.

**Time: ** 20. May 2022, 11:00h

**Place: ** Faculty of Physics, room 665, and online

**Speaker: ** Marko Vojinovic

**Title: ** A review of a few results at the interplay between quantum gravity and quantum information theory

**Abstract:**

I will give a review of two (if time permits maybe three) results obtained in collaboration with Nikola Paunkovic, on research at the intersection between quantum gravity (QG) and quantum information theory (QI). The first result deals with the possible space of states in an abstract QG formalism, and the restrictions imposed by gauge symmetry, specifically diffeomorphisms. It turns out that these restrictions generically rule out gravity-matter product states as gauge-noninvariant. The second result deals with the motion of a point-particle in QG, in particular in a background gravitational field constructed as a quantum superposition of two distinct spacetime geometries. The resulting trajectory of the particle fails to be described by a geodesic equation with respect to either geometry, giving rise to a correction term due to quantum interference between two geometries. We will discuss the consequences of this for the weak equivalence principle. Finally, we may briefly mention a few other recent results trending in the QI community, such as the quantum switch protocol, del Santo-Dakic protocol, and their relationship to QG.

**Time: ** 29. April 2022, 11:00h

**Place: ** Faculty of Physics, room 665, and online

**Speaker: ** Mihailo Djordjevic

**Title: ** Coleman-Mandula theorem

**Abstract:**

Coleman-Mandula theorem is a no-go theorem in theoretical physics. It states that space-time symmetries and internal symmetries cannot be combined in any but a trivial way. The main consequence of the theorem is impossibility of finding functional dependence between parameters of irreducible representations of the Poincaré group (mass and spin), and parameters of irreducible representations of internal symmetry group (charge, color etc.). Finding a "loophole" of the theorem would give a new insight into the relations between properties of elementary particles, and by doing that, it would also reduce the number of fundamental constants of the theory. In this seminar, we will give a precise formulation of the theorem, show its detailed proof based on very general physical assumptions and talk about possible ways of the generalization of the theorem and of "loopholing" it.

**Time: ** 15. April 2022, 11:00h

**Place: ** Faculty of Physics, room 665, and online

**Speaker: ** Dusan Djordjevic

**Title: ** Noncommutative D=5 Chern-Simons gravity: Kaluza-Klein reduction and chiral gravitational anomaly

**Abstract:**

Chern-Simons (CS) theory has greatly influenced physics and physicists during the past half-century. In this seminar, we will review some basic facts about Chern-Simons Lagrangians defined on some (2n-1)-dimensional manifold. We will then show how CS theory can be connected with gravity. Our focus will be on an SO(4,2) CS gravity in five dimensions and its connections with four-dimensional gravitation. Furthermore, we will analyse the noncommutative deformation of SO(4,2) CS gravity using the geometric Seiberg-Witten map. This theory has a nontrivial first-order correction in \theta. By performing Kaluza-Klein dimensional reduction and suitable symmetry breaking, we obtain an effective, four-dimensional gravity theory that has Einstein-Hilbert action with (negative) cosmological constant as its classical (commutative) limit. We then proceed to analyse some concrete solutions of the field equations. We show that AdS space-time remains a solution after including the first-order corrections. On the other hand, AdS-Schwarzschild black hole solution develops a torsion that we explicitly compute. Moreover, we will see that this modified solution implies the existence of a chiral gravitational anomaly if one couples massless Dirac fermions to this NC background.

Based on arXiv:2203.05020.

**Time: ** 1. April 2022, 11:00h

**Place: ** Faculty of Physics, room 661, and online

**Speaker: ** Branislav Cvetkovic

**Title: ** Entropy in Poincaré gauge theory: Hamiltonian approach (part 2)

**Abstract:**

Canonical generator G of local symmetries in Poincaré gauge theory is constructed as an integral over a spatial section Σ of spacetime. Its regularity (differentiability) on the phase space is ensured by adding a suitable surface term, an integral over the boundary of Σ at infinity, which represents the asymptotic canonical charge. For black hole solutions, Σ has two boundaries, one at infinity and the other at horizon. It is shown that the canonical charge at horizon defines entropy, whereas the regularity of G implies the first law of black hole thermodynamics.

**Time: ** 25. March 2022, 11:00h

**Place: ** Faculty of Physics, room 661, and online

**Speaker: ** Branislav Cvetkovic

**Title: ** Entropy in Poincaré gauge theory: Hamiltonian approach (part 1)

**Abstract:**

Canonical generator G of local symmetries in Poincaré gauge theory is constructed as an integral over a spatial section Σ of spacetime. Its regularity (differentiability) on the phase space is ensured by adding a suitable surface term, an integral over the boundary of Σ at infinity, which represents the asymptotic canonical charge. For black hole solutions, Σ has two boundaries, one at infinity and the other at horizon. It is shown that the canonical charge at horizon defines entropy, whereas the regularity of G implies the first law of black hole thermodynamics.

**Time: ** 11. March 2022, 11:00h

**Place: ** Online

**Speaker: ** Igor Prlina

**Title: ** Landau singularities in planar massless theories

**Abstract:**

In this work we present our contribution to the method of using Landau singularities for probing scattering amplitudes in planar massless quantum field theories. We start by proposing a simple geometric algorithm for determining the complete set of branch points of amplitudes in planar N = 4 super-Yang-Mills theory directly from the amplituhedron, without resorting to any particular representation in terms of local Feynman integrals. This represents a step towards translating integrands directly into integrals. In particular, the algorithm provides information about the symbol alphabets of general amplitudes. First we illustrate the algorithm applied to the one- and two-loop MHV amplitudes. Then we demonstrate how to use the reformulation of amplituhedra in terms of 'sign flips' in order to streamline the application of this algorithm to amplitudes of any helicity. In this way we recover the known branch points of all one-loop amplitudes, and we find an 'emergent positivity' on boundaries of amplituhedra. Lastly, we look beyond planar N = 4 super-Yang-Mills theory, and analyze Landau singularities of general massless planar theories. In massless quantum field theories the Landau equations are invariant under graph operations familiar from the theory of electrical circuits. Using a theorem on the Y-∆ reducibility of planar circuits we prove that the set of first-type Landau singularities of an n-particle scattering amplitude in any massless planar theory, in any spacetime dimension D, at any finite loop order in perturbation theory, is a subset of those of a certain n-particle ⌊(n−2)^2/4⌋-loop "ziggurat" graph. We determine this singularity locus explicitly for D = 4 and n = 6 and find that it corresponds precisely to the vanishing of the symbol letters familiar from the hexagon bootstrap in SYM theory. Further implications for SYM theory are discussed.

**Time: ** 25. February 2022, 11:00h

**Place: ** Online

**Speaker: ** Ilija Ivanisevic

**Title: ** Courant algebroids in bosonic string theory (part 2)

**Abstract:**

We analyze bosonic string symmetry transformations and their relations with T-duality in the framework of generalized geometry. The generator governing symmetry transformations can be described simply as the inner product of generalized vectors and its algebra produces the Courant bracket as the T-dual invariant extension of the Lie bracket, while T-duality can be interpreted as an isomorphism between Courant algebroids. We show how different O(D,D) transformations give rise to different twists of the Courant bracket that feature string theory relevant fluxes.

Based on arXiv:1903.04832, arXiv:2010.1066, arXiv:2103.09585 and arXiv:2202.03227.

**Time: ** 18. February 2022, 11:00h

**Place: ** Online

**Speaker: ** Ilija Ivanisevic

**Title: ** Courant algebroids in bosonic string theory (part 1)

**Abstract:**

We analyze bosonic string symmetry transformations and their relations with T-duality in the framework of generalized geometry. The generator governing symmetry transformations can be described simply as the inner product of generalized vectors and its algebra produces the Courant bracket as the T-dual invariant extension of the Lie bracket, while T-duality can be interpreted as an isomorphism between Courant algebroids. We show how different O(D,D) transformations give rise to different twists of the Courant bracket that feature string theory relevant fluxes.

Based on arXiv:1903.04832, arXiv:2010.1066, arXiv:2103.09585 and arXiv:2202.03227.

**Time: ** 4. February 2022, 11:00h

**Place: ** Online

**Speaker: ** Dragan Prekrat

**Title: ** Phase transitions in matrix models on the truncated Heisenberg space

**Abstract:**

The important generic problem with QFTs on noncommutative spaces is the UV/IR mixing of divergences which interferes with their renormalization. The Grosse-Wulkenhaar model solved this problem by introducing a harmonic oscillator term that can be interpreted as a coupling between the curvature and the field. In this talk, we will examine the success of this model from the phase transition point of view. We will show that renormalizable and nonrenormalizable versions of the 2D noncommutative phi4 model have different phase diagrams. We will also consider the implications of the striped-phase shifting on the renormalization properties of other models.

Based on arXiv:2104.00657 and arXiv:2002.05704.

**Time: ** 21. January 2022, 11:00h

**Place: ** Faculty of Physics, room 661, and online

**Speaker: ** Bojana Brkic

**Title: ** Laplacian on fuzzy de Sitter space

**Abstract:**

In this seminar, we shall consider the geometric property of fuzzy de Sitter space by studying the Laplacian. The latter is defined within the noncommutative frame formalism and it is not hermitian, thus, inducing the nonunitary evolution. We shall solve the eigenproblem of the symmetrically ordered quantum-mechanical Laplacian and discuss its spectrum.

**Seminars for the year:**
2024
2023
2022
2021
2020
2019
2018
2017
2016
2015
2014
2013
2012
2011
2010
2009
2008
2007

**Follow our seminars online via:** GPF BigBlueButton server