Engineering topics

Dimofte, Tudor

Publications and source records attributed to Dimofte, Tudor.

8 records

DOE OSTI2019

(0,2) dualities and the 4-simplex

We propose that a simple, Lagrangian 2d $ \mathcal{N} $ = (0, 2) duality interface between the 3d $ \mathcal{N} $ = 2 XYZ model and 3d $ \mathcal{N} $ = 2 SQED can be associated to the simplest triangulated 4-manifold: the 4-simplex. We then begin to flesh out a dictionary between more general triangulated 4-manifolds with boundary and 2d $ \mathcal{N} $ = (0, 2) interfaces. In particular, we identify IR dualities of interfaces associated to local changes of 4d triangulation, governed by the (3), (2, 4), and (2, 4) Pachner moves. We check these dualities using supersymmetric half-indices. We also describe how to produce stand-alone 2d theories (as opposed to interfaces) capturing the geometry of 4-simplices and Pachner moves by making additional field-theoretic choices, and find in this context that the Pachner moves recover abelian $ \mathcal{N} $ = (0, 2) trialities of Gadde-Gukov-Putrov. Our work provides new, explicit tools to explore the interplay between 2d dualities and 4-manifold geometry that has been developed in recent years.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2018

Dual boundary conditions in 3d SCFT’s

We propose matching pairs of half-BPS boundary conditions related by IR dualities of 3d $\mathcal{N}$=2 gauge theories. From these matching pairs we construct duality interfaces. We test our proposals by anomaly matching and the computation of supersymmetric indices. With this being said, examples include basic abelian dualities, level-rank dualities, and Aharony dualities.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2018

Quantum modularity and complex Chern-Simons theory

The Quantum Modularity Conjecture of Zagier predicts the existence of a formal power series with arithmetically interesting coefficients that appears in the asymptotics of the Kashaev invariant at each root of unity. Our goal is to construct a power series from a Neumann-Zagier datum (i.e., an ideal triangulation of the knot complement and a geometric solution to the gluing equations) and a complex root of unity $\zeta$. We prove that the coefficients of our series lie in the trace field of the knot, adjoined a complex root of unity. We conjecture that our series are those that appear in the Quantum Modularity Conjecture and confirm that they match the numerical asymptotics of the Kashaev invariant (at various roots of unity) computed by Zagier and the first author. Our construction is motivated by the analysis of singular limits in Chern-Simons theory with gauge group $SL(2,C)$ at fixed level $k$, where $\zeta^k=1$.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2017

The Coulomb Branch of 3d $${\mathcal{N}= 4}$$ N = 4 Theories

We propose a construction for the quantum-corrected Coulomb branch of a general 3d gauge theory with N=4 supersymmetry, in terms of local coordinates associated with an abelianized theory. In a fixed complex structure, the holomorphic functions on the Coulomb branch are given by expectation values of chiral monopole operators. We construct the chiral ring of such operators, using equivariant integration over BPS moduli spaces. We also quantize the chiral ring, which corresponds to placing the 3d theory in a 2d Omega background. Then, by unifying all complex structures in a twistor space, we encode the full hyperkähler metric on the Coulomb branch. We verify our proposals in a multitude of examples, including SQCD and linear quiver gauge theories, whose Coulomb branches have alternative descriptions as solutions to Bogomolnyi and/or Nahm equations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2016

K-decompositions and 3d gauge theories

This paper combines several new constructions in mathematics and physics. Mathematically, we study framed flat PGL(K, C)-connections on a large class of 3-manifolds M with boundary. We introduce a moduli space $\mathcal{L}$ K (M) of framed flat connections on the boundary ∂M that extend to M. Our goal is to understand an open part of $\mathcal{L}$ K (M) as a Lagrangian subvariety in the symplectic moduli space X un K (∂M) of framed flat connections on the boundary — and more so, as a “K 2 -Lagrangian,” meaning that the K 2 -avatar of the symplectic form restricts to zero. We construct an open part of $\mathcal{L}$ K (M) from elementary data associated with the hypersimplicial K-decomposition of an ideal triangulation of M, in a way that generalizes (and combines) both Thurston’s gluing equations in 3d hyperbolic geometry and the cluster coordinates for framed flat PGL(K, C)-connections on surfaces. By using a canonical map from the complex of configurations of decorated flags to the Bloch complex, we prove that any generic component of $\mathcal{L}$ K (M) is K 2 -isotropic as long as ∂M satisfies certain topological constraints (theorem 4.2). In some cases this easily implies that $\mathcal{L}$ K (M) is K 2 -Lagrangian. For general M, we extend a classic result of Neumann and Zagier on symplectic properties of PGL(2) gluing equations to reduce the K 2 -Lagrangian property to a combinatorial statement. Physically, we translate the K-decomposition of an ideal triangulation of M and its symplectic properties to produce an explicit construction of 3d N = 2 superconformal field theories T K [M] resulting (conjecturally) from the compactification of K M5-branes on M. This extends known constructions for K = 2. Just as for K = 2, the theories T K [M] are described as IR fixed points of abelian Chern-Simons-matter theories. Changes of triangulation (2-3 moves) lead to abelian mirror symmetries that are all generated by the elementary duality between N f = 1 SQED and the XYZ model. In the large K limit, we find evidence that the degrees of freedom of T K [M] grow cubically in K.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2016

Boundaries, mirror symmetry, and symplectic duality in 3d N = 4 gauge theory

We introduce several families of N = (2, 2) UV boundary conditions in 3d N=4 gauge theories and study their IR images in sigma-models to the Higgs and Coulomb branches. In the presence of Omega deformations, a UV boundary condition defines a pair of modules for quantized algebras of chiral Higgs- and Coulomb-branch operators, respectively, whose structure we derive. In the case of abelian theories, we use the formalism of hyperplane arrangements to make our constructions very explicit, and construct a half-BPS interface that implements the action of 3d mirror symmetry on gauge theories and boundary conditions. Finally, by studying two-dimensional compactifications of 3d N = 4 gauge theories and their boundary conditions, we propose a physical origin for symplectic duality $-$ an equivalence of categories of modules associated to families of Higgs and Coulomb branches that has recently appeared in the mathematics literature, and generalizes classic results on Koszul duality in geometric representation theory. We make several predictions about the structure of symplectic duality, and identify Koszul duality as a special case of wall crossing.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2016

3d-3d correspondence revisited

In fivebrane compactifications on 3-manifolds, we point out the importance of all flat connections in the proper definition of the effective 3d N = 2 theory. The Lagrangians of some theories with the desired properties can be constructed with the help of homological knot invariants that categorify colored Jones polynomials. Higgsing the full 3d theories constructed this way recovers theories found previously by Dimofte-Gaiotto-Gukov. As a result, we also consider the cutting and gluing of 3-manifolds along smooth boundaries and the role played by all flat connections in this operation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2015

Complex Chern–Simons Theory at Level k via the 3d–3d Correspondence

Herein, we use the 3d–3d correspondence together with the DGG construction of theories T n [ M ] labelled by 3-manifolds M to define a non-perturbative state-integral model for ${SL(n,\mathbb{C})}$ Chern–Simons theory at any level k , based on ideal triangulations. The resulting partition functions generalize a widely studied k = 1 state-integral, as well as the 3d index, which is k = 0. The Chern–Simons partition functions correspond to partition functions of T n [ M ] on squashed lens spaces L ( k , 1). At any k , they admit a holomorphic-antiholomorphic factorization, corresponding to the decomposition of L ( k , 1) into two solid tori, and the associated holomorphic block decomposition of the partition functions of T n [ M ]. A generalization to L ( k , p ) is also introduced. Convergence of the state integrals, for any k , requires triangulations to admit a positive angle structure; we propose that this is also necessary for the DGG gauge theory T n [ M ] to flow to a desired IR SCFT.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗