Title: Universality and Application of fRG for Combinatorial Models
Speaker:Arslan Sikandar
Location: 29#414
Time: Every Friday (starting firstly on March 7th) starts at 8;00am
Abstract:The solvability of O(N)models [l] at large-N is quantified and comparedwith the upper bounds set by conformal bootstrap[2]. The large-N limitalong with the double scaling limit is then discussed for extensions of randommatrix models called the colored tensor models. Rank-4 real colored tensormodels are studied including the diagrammatics. The functional renormal-ization group(fRG) equation is derived for such combinatorial systems andvarious issues related to infrared regulator and truncation is discussed[3]The search for relevant critical exponents is done and a hypothesis is madeof relating it to the universality class of a pure gravity theory with highercurvature terms [4].
Talk 2（March 14th）
In this talk, I will discuss the path integral approach to quantum field theory. We will start with the partition function ZI as a generating functional to generate Green's function for a relativistic scalar field theory.
Talk 3（March 21st）
I will continue and introduce conncected Green's fuction via a new Generating functional W=-Z. The corresponding Feynman diagrams will be ex-tracted from the Green's function.
Talk 4（March 28th）
We will take Legendre's transform of the connected Generating functional W.to introduce a new quantity called effective action functional pe. The 2-pointand 3-point vertex functions are derived.
Talk 5（April 11th）
After having introduced the effective action , we will derive the exact fowequation of it a.k.a Wetterich Equation in context of functional RenormalizationGroup(fRG). Various subtleties will be discussed.
Talk 6（April 18th）
In this talk we will explore Berezinskii-Kosterlitz-Thouless (BKT) Transition from XY model in 2 dimensions. How is it realized in various bosonic and fermionic systems.
References:
[1] M. Moshe and J. Zinn-Justin, Quantum feld theory in the large N limit: A Review, Phys. Rep. 385, 69-228 (2003), arXiv:hep-th/0306133
[2] F. Kos, D. Poland, and D. Simmons-Dufin, Bootstrapping the O(N) vector models, JHEP 1406, 091 (2014), arXiv:1307.6856
[3] A. Eichhorn, J. Lumma, A. D. Pereira, and A. Sikandar, JHEP 02, 110 (2020), arXiv:1912.05314
[4] K. Falls, D.F. Litim, K. Nikolakopoulos, and C. Rahmede, Phys. Rev. D 93,104022 (2016)
