Novel Aspects of 3D N= 2 Chern–Simons–Matter theories

Khlaif, Osama K. F. ORCID: 0000-0001-5898-3028 (2025). Novel Aspects of 3D N= 2 Chern–Simons–Matter theories. University of Birmingham. Ph.D.

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Abstract

In this thesis, we explore new results we recently obtained about the infrared physics of 3d N= 2 SQCD with a unitary gauge group, in particular in the presence of a non-zero Fayet–Iliopoulos (FI) parameter and with generic values of the Chern–Simons levels. We study the 3d gauged linear sigma model (GLSM) (also known as 3d A-model) approach to the computation of the 3d N = 2 twisted chiral ring of half-BPS lines. We analyse the moduli space of supersymmetric vacua in the theory, and we study its dependence on the Chern–Simons levels and the sign of the FI parameter. For particular values of the Chern–Simons levels, the twisted chiral ring has a neat interpretation in terms of the quantum K-theory (QK) of the complex Grassmannian variety. We propose a new set of linedefectsofthe3dgaugetheory,dubbedGrothendiecklines,whichrepresentequivariant Schubert classes in the QK ring. In particular, we show that the double Grothendieck polynomials, which represent the equivariant Chern characters of the Schubert classes, arise physically as Witten indices of certain quiver supersymmetric quantum mechanics. We also explain two distinct ways to compute K-theoretic enumerative invariants using the 3d GLSM approach. Moreover, we study infrared dualities associated with these 3d SQCDs. We use our techniques and analysis to test these dualities and, for some cases, we give a geometric interpretation for these dualities.

Type of Work:

Thesis (Doctorates > Ph.D.)

Award Type:

Doctorates > Ph.D.

Supervisor(s):