Engineering topics

Nekrasov, Nikita

Publications and source records attributed to Nekrasov, Nikita.

3 records

DOE OSTI2024

Global Magni4icence, or: 4G Networks

The global magnificent four theory is the homological version of a maximally supersymmetric $(8+1)$-dimensional gauge theory on a Calabi-Yau fourfold fibered over a circle. In the case of a toric fourfold we conjecture the formula for its twisted Witten index. String-theoretically we count the BPS states of a system of $D0$-$D2$-$D4$-$D6$-$D8$-branes on the Calabi-Yau fourfold in the presence of a large Neveu-Schwarz $B$-field. Mathematically, we develop the equivariant $K$-theoretic DT4 theory, by constructing the four-valent vertex with generic plane partition asymptotics. Physically, the vertex is a supersymmetric localization of a non-commutative gauge theory in $8+1$ dimensions.

Mathematics↗

DOE OSTI2021

Intersecting defects in gauge theory, quantum spin chains, and Knizhnik-Zamolodchikov equations

We propose an interesting BPS/CFT correspondence playground: the correlation function of two intersecting half-BPS surface defects in four-dimensional N = 2 supersymmetric SU(N) gauge theory with 2N fundamental hypermultiplets. We show it satisfies a difference equation, the fractional quantum T-Q relation. Its Fourier transform is the 5-point conformal block of the sl N current algebra with one of the vertex operators corresponding to the N-dimensional sl N representation, which we demonstrate with the help of the Knizhnik-Zamolodchikov equation. We also identify the correlator with a state of the XXX sl 2 spin chain of N Heisenberg-Weyl modules over Y (sl 2 ). We discuss the associated quantum Lax operators, and connections to isomonodromic deformations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Riemann-Hilbert correspondence and blown up surface defects

The relationship of two dimensional quantum field theory and isomonodromic deformations of Fuchsian systems has a long history. Recently four-dimensional N = 2 gauge theories joined the party in a multitude of roles. In this paper we study the vacuum expectation values of intersecting half-BPS surface defects in SU(2) theory with N f = 4 fundamental hypermultiplets. We show they form a horizontal section of a Fuchsian system on a sphere with 5 regular singularities, calculate the monodromy, and define the associated isomonodromic tau-function. Using the blowup formula in the presence of half-BPS surface defects, initiated in the companion paper, we obtain the GIL formula, establishing an unexpected relation of the topological string/free fermion regime of supersymmetric gauge theory to classical integrability.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗