Publication

Quantum loop groups and K$K$‐theoretic stable envelopes

Andrei Negut
2025

Abstract

We develop the connection between the preprojective ‐theoretic Hall algebra [Schiffmann and Vasserot (Duke Math. J. 162 (2013), no. 2, 279–366), Yang and Zhao (Proc. London Math. Soc. (3) 116 (2018), no. 5, 1029–1074)] of a quiver and the quantum loop group associated to via stable envelopes of Nakajima quiver varieties [Okounkov and Smirnov (Invent. Math. 229 (2022), 1203–1299)].

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Andrei Negut
2025

Abstract

Official source

Related concepts (8)

Loop quantum gravity

Loop quantum gravity (LQG) is a theory of quantum gravity, which aims to reconcile quantum mechanics and general relativity, incorporating matter of the Standard Model into the framework established for the intrinsic quantum gravity case. It is an attempt to develop a quantum theory of gravity based directly on Einstein's geometric formulation rather than the treatment of gravity as a mysterious mechanism (force). As a theory LQG postulates that the structure of space and time is composed of finite loops woven into an extremely fine fabric or network.

Quantum gravity

Quantum gravity (QG) is a field of theoretical physics that seeks to describe gravity according to the principles of quantum mechanics. It deals with environments in which neither gravitational nor quantum effects can be ignored, such as in the vicinity of black holes or similar compact astrophysical objects, such as neutron stars as well as in the early stages of the universe moments after the Big Bang Three of the four fundamental forces of nature are described within the framework of quantum mechanics and quantum field theory: the electromagnetic interaction, the strong force, and the weak force; this leaves gravity as the only interaction that has not been fully accommodated.

Quantum chromodynamics

In theoretical physics, quantum chromodynamics (QCD) is the theory of the strong interaction between quarks mediated by gluons. Quarks are fundamental particles that make up composite hadrons such as the proton, neutron and pion. QCD is a type of quantum field theory called a non-abelian gauge theory, with symmetry group SU(3). The QCD analog of electric charge is a property called color. Gluons are the force carriers of the theory, just as photons are for the electromagnetic force in quantum electrodynamics.