**Seminars for the year:**
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**Time: ** 7. May 2021, 11:15h

**Place: ** Institute of Physics, online

**Speaker: ** Grigorios Giotopoulos

**Title: ** Braided gauge field theory: New examples

**Abstract:**

In this talk I will be presenting new examples of braided field theories, via braided L-infinity algebras. First, I will briefly review how L-infinity algebras appear in classical field theory and how Drinfel'd twists work in practice. I will then apply the braided L-infinity algebra framework for the cases of scalar field, BF and Yang-Mills theories and remark on the features of the resulting noncommutative theories.

**Time: ** 16. April 2021, 11:15h

**Place: ** Institute of Physics, online

**Speaker: ** Marija Dimitrijevic Ciric

**Title: ** Application of L-infinity Algebras: Braided Deformation of Field Theory and Noncommutative Gravity (part 3)

**Abstract:**

In this talk we discuss a possibility to apply the L-infinity algebra formalism in construction of field theories and gravity on noncommutative spaces. To do this we have to introduce a new homotopy algebraic structure, that we call a braided L-infinity algebra. Then we use the braided L-infinity algebra to systematically construct a new class of noncommutative field theories, that we call braided field theories. Braided field theories have gauge symmetries which realize a braided Lie algebra, whose Noether identities are inhomogeneous extensions of the classical identities, and which do not act (in a standard/obvious way) on the solutions of the field equations.

In the first talk we will motivate the introduction of braided gauge field theories and we will repeat the basics of the twist deformation formalism introduced by Drinfeld in 1985.

In the second talk we will define braided gauge theories and discuss how they fit in the braided L-inifinity algebra formalism. Finally, we will present two examples: braided Chern-Simons theory and braided Einstein-Cartan-Palatini 4D gravity.

The lecture is based on the following papers:

[1] M. Dimitrijevic Ciric, G. Giotopoulos, V. Radovanovic, R. J. Szabo, "$L_\infty$-Algebras of Einstein-Cartan-Palatini Gravity", *Jour. Math. Phys.* **61**, 112502 (2020), [arXiv:2003.06173].

[2] M. Dimitrijevic Ciric, G. Giotopoulos, V. Radovanovic, R. J. Szabo, "Braided $L_\infty$-Algebras, Braided Field Theory and Noncommutative Gravity", [arXiv:2103.08939].

**Time: ** 09. April 2021, 11:15h

**Place: ** Institute of Physics, online

**Speaker: ** Marija Dimitrijevic Ciric

**Title: ** Application of L-infinity Algebras: Braided Deformation of Field Theory and Noncommutative Gravity (part 2)

**Abstract:**

In this talk we discuss a possibility to apply the L-infinity algebra formalism in construction of field theories and gravity on noncommutative spaces. To do this we have to introduce a new homotopy algebraic structure, that we call a braided L-infinity algebra. Then we use the braided L-infinity algebra to systematically construct a new class of noncommutative field theories, that we call braided field theories. Braided field theories have gauge symmetries which realize a braided Lie algebra, whose Noether identities are inhomogeneous extensions of the classical identities, and which do not act (in a standard/obvious way) on the solutions of the field equations.

In the first talk we will motivate the introduction of braided gauge field theories and we will repeat the basics of the twist deformation formalism introduced by Drinfeld in 1985.

In the second talk we will define braided gauge theories and discuss how they fit in the braided L-inifinity algebra formalism. Finally, we will present two examples: braided Chern-Simons theory and braided Einstein-Cartan-Palatini 4D gravity.

The lecture is based on the following papers:

[1] M. Dimitrijevic Ciric, G. Giotopoulos, V. Radovanovic, R. J. Szabo, "$L_\infty$-Algebras of Einstein-Cartan-Palatini Gravity", *Jour. Math. Phys.* **61**, 112502 (2020), [arXiv:2003.06173].

[2] M. Dimitrijevic Ciric, G. Giotopoulos, V. Radovanovic, R. J. Szabo, "Braided $L_\infty$-Algebras, Braided Field Theory and Noncommutative Gravity", [arXiv:2103.08939].

**Time: ** 02. April 2021, 11:15h

**Place: ** Institute of Physics, online

**Speaker: ** Marija Dimitrijevic Ciric

**Title: ** Application of L-infinity Algebras: Braided Deformation of Field Theory and Noncommutative Gravity (part 1)

**Abstract:**

In this talk we discuss a possibility to apply the L-infinity algebra formalism in construction of field theories and gravity on noncommutative spaces. To do this we have to introduce a new homotopy algebraic structure, that we call a braided L-infinity algebra. Then we use the braided L-infinity algebra to systematically construct a new class of noncommutative field theories, that we call braided field theories. Braided field theories have gauge symmetries which realize a braided Lie algebra, whose Noether identities are inhomogeneous extensions of the classical identities, and which do not act (in a standard/obvious way) on the solutions of the field equations.

In the first talk we will motivate the introduction of braided gauge field theories and we will repeat the basics of the twist deformation formalism introduced by Drinfeld in 1985.

In the second talk we will define braided gauge theories and discuss how they fit in the braided L-inifinity algebra formalism. Finally, we will present two examples: braided Chern-Simons theory and braided Einstein-Cartan-Palatini 4D gravity.

The lecture is based on the following papers:

[1] M. Dimitrijevic Ciric, G. Giotopoulos, V. Radovanovic, R. J. Szabo, "$L_\infty$-Algebras of Einstein-Cartan-Palatini Gravity", *Jour. Math. Phys.* **61**, 112502 (2020), [arXiv:2003.06173].

[2] M. Dimitrijevic Ciric, G. Giotopoulos, V. Radovanovic, R. J. Szabo, "Braided $L_\infty$-Algebras, Braided Field Theory and Noncommutative Gravity", [arXiv:2103.08939].

**Time: ** 26. March 2021, 11:15h

**Place: ** Institute of Physics, online

**Speaker: ** Clay Grewcoe

**Title: ** Curved L-infinity algebras

**Abstract:**

What are curved L-infinity algebras? This less common but very natural generalisation will be theoretically defined and explored through the example of a DFT algebroid, the geometric structure underlying the sigma model of double field theory. Additionally, it will be explored how and in what cases one can "flatten" a curved L-infinity algebra into a regular one.

The lecture is based on the following paper:

[1] C. J. Grewcoe and L. Jonke, "DFT algebroid and curved $L_\infty$-algebras", [arXiv:2012.02712].

**Time: ** 19. March 2021, 11:15h

**Place: ** Institute of Physics, online

**Speaker: ** Clay Grewcoe

**Title: ** BV/BRST formalism in the language of L-infinity algebras

**Abstract:**

Batalin-Vilkovisky procedure is an important part of gauge field theories, and given the connection between field theory and L-infinity algebras demonstrated in previous lectures, it is natural to ask how does the BV formalism fit into that picture. In order to discuss this one needs to define a tensor product of L-infinity algebras and use it to connect the gauge symmetry with classical field theory and further with its BV (BRST) extension. As an example we will use the Courant sigma model as a theory which displays all properties of the formalism.

The lecture is based on the following papers:

[1] C. J. Grewcoe and L. Jonke, "Courant Sigma Model and $L_\infty$-algebras", *Fortsch. Phys.* **68** no.6, 2000021 (2020) [arXiv:2001.11745].

[2] B. Jurčo, L. Raspollini, C. Saemann and M. Wolf, "$L_\infty$-Algebras of Classical Field Theories and the Batalin-Vilkovisky Formalism", *Fortsch. Phys.* **67** no.7, 1900025 (2019) [arXiv:1809.09899].

**Time: ** 12. March 2021, 11:15h

**Place: ** Institute of Physics, online

**Speaker: ** Voja Radovanovic

**Title: ** L-infinity algebras and field theory (part 2)

**Abstract:**

In this series of lectures we will analyze in detail L-infinity algebras and their application in field theory and gravity on commutative and noncommutative spaces. We will begin by introducing a concept of L-infinity algebra as a generalization of the usual concept of Lie algebra. Then we will discuss in detail four examples: Yang-Mills gauge theory, Eintein-Cartan-Palatini gravity, BRST symmetry and Chern-Simons gauge theory. All these examples are examples of field theory on the commutative spacetime. The material presented here will be generalized later on (in the following seminars) to field theories on noncommutative spaces.

**Time: ** 5. March 2021, 11:15h

**Place: ** Institute of Physics, online

**Speaker: ** Voja Radovanovic

**Title: ** L-infinity algebras and field theory (part 1)

**Abstract:**

In this series of lectures we will analyze in detail L-infinity algebras and their application in field theory and gravity on commutative and noncommutative spaces. We will begin by introducing a concept of L-infinity algebra as a generalization of the usual concept of Lie algebra. Then we will discuss in detail four examples: Yang-Mills gauge theory, Eintein-Cartan-Palatini gravity, BRST symmetry and Chern-Simons gauge theory. All these examples are examples of field theory on the commutative spacetime. The material presented here will be generalized later on (in the following seminars) to field theories on noncommutative spaces.

**Time: ** 19. February 2021, 11:15h

**Place: ** Institute of Physics, online

**Speaker: ** Igor Salom

**Title: ** Ortosymplectic superalgebra as a spacetime symmetry (part 2)

**Abstract:**

We will explain the relationship between the orthosymplectic algebra osp(1|8) and the Poincaré and conformal (super)symmetry, and we will demonstrate why this symmetry is also called generalized superconformal symmetry. We will discuss unitary irreducible representations of this algebra, with a focus on the simplest such representations. It will turn out that the simplest representation corresponds to the space of a massless relativistic particle which, depending on helicity, automatically and inevitably satisfies appropriate equations of motion (such as Klein-Gordon, Dirac, or Maxwell equations). Special attention will be devoted to the appearence of the the EM duality symmetry in this context. We will also consider the first next (least complex) representation, and see that it corresponds to massive particles, with two mass terms appearing, which are mutually related by EM duality symmetry.

**Time: ** 12. February 2021, 11:15h

**Place: ** Institute of Physics, online

**Speaker: ** Igor Salom

**Title: ** Ortosymplectic superalgebra as a spacetime symmetry (part 1)

**Abstract:**

We will explain the relationship between the orthosymplectic algebra osp(1|8) and the Poincaré and conformal (super)symmetry, and we will demonstrate why this symmetry is also called generalized superconformal symmetry. We will discuss unitary irreducible representations of this algebra, with a focus on the simplest such representations. It will turn out that the simplest representation corresponds to the space of a massless relativistic particle which, depending on helicity, automatically and inevitably satisfies appropriate equations of motion (such as Klein-Gordon, Dirac, or Maxwell equations). Special attention will be devoted to the appearence of the the EM duality symmetry in this context. We will also consider the first next (least complex) representation, and see that it corresponds to massive particles, with two mass terms appearing, which are mutually related by EM duality symmetry.

**Time: ** 29. January 2021, 11:00h

**Place: ** Institute of Physics, online

**Speaker: ** Tijana Radenkovic

**Title: ** Gauge symmetry of the 3BF theory for a generic Lie 3-group

**Abstract:**

The higher category theory can be employed to generalize the BF action to the so-called 3BF action, by passing from the notion of a gauge group to the notion of a gauge 3-group. In this work we determine the full gauge symmetry of the 3BF action. To that end, the complete Hamiltonian analysis of the 3BF action for a general Lie 3-group is performed, by using the Dirac procedure. This analysis is the first step towards a canonical quantization of a 3BF theory. This is an important stepping-stone for the quantization of the complete Standard Model of elementary particles coupled to Einstein-Cartan gravity, formulated as a 3BF action with suitable simplicity constraints. We show that the resulting gauge symmetry group consists of the already familiar G-, H-, and L-gauge transformations, as well as additional M- and N-gauge transformations, which have not been discussed in the existing literature.

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

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