scholarly journals Superconformal Line Defects in 3D

Universe ◽  
2021 ◽  
Vol 7 (9) ◽  
pp. 348
Author(s):  
Silvia Penati
Keyword(s):  
Three Dimensional ◽  
Fundamental Relation ◽  
Abjm Theory ◽  
Superconformal Field Theories ◽  
Conformal Bootstrap ◽  
Topological Quantum ◽  
Exact Evaluation ◽  
Line Defects ◽  
Chern Simons ◽  
Physical Quantities

We review the recent progress in the study of line defects in three-dimensional Chern–Simons-matter superconformal field theories, notably the ABJM theory. The first part is focused on kinematical defects, supporting a topological sector of the theory. After reviewing the construction of this sector, we concentrate on the evaluation of topological correlators from the partition function of the mass-deformed ABJM theory and provide evidence on the existence of topological quantum mechanics living on the line. In the second part, we consider the dynamical defects realized as latitude BPS Wilson loops for which an exact evaluation is available in terms of a latitude Matrix Model. We discuss the fundamental relation between these operators, the defect superconformal field theory and bulk physical quantities, such as the Bremsstrahlung function. This relation assigns a privileged role to BPS Wilson operators, which become the meeting point for three exact approaches: localization, integrability and conformal bootstrap.

scholarly journals On a gravity dual to flavored topological quantum mechanics

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Andrey Feldman
Keyword(s):  
Quantum Mechanics ◽  
Effective Field ◽  
Abjm Theory ◽  
Yang Mills ◽  
Topological Quantum ◽  
Higher Derivatives ◽  
Structure Constants ◽  
Holographic Description ◽  
M Theory ◽  
Chern Simons

Abstract In this paper, we propose a generalization of the AdS2/CFT1 correspondence constructed by Mezei, Pufu and Wang in [1], which is the duality between 2d Yang-Mills theory with higher derivatives in the AdS2 background, and 1d topological quantum mechanics of two adjoint and two fundamental U(N ) fields, governing certain protected sector of operators in 3d ABJM theory at the Chern-Simons level k = 1. We construct a holographic dual to a flavored generalization of the 1d quantum mechanics considered in [1], which arises as the effective field theory living on the intersection of stacks of N D2-branes and k D6-branes in the Ω-background in Type IIA string theory, and describes the dynamics of the protected sector of operators in $$ \mathcal{N} $$ N = 4 theory with k fundamental hypermultiplets, having a holographic description as M-theory in the AdS4× S7/ℤk background. We compute the structure constants of the bulk theory gauge group, and construct a map between the observables of the boundary theory and the fields of the bulk theory.

scholarly journals CHERN–SIMONS APPROACH TO THREE-MANIFOLD INVARIANTS

1995 ◽  
Vol 10 (06) ◽  
pp. 487-493
Author(s):  
BOGUSŁAW BRODA
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Lie Group ◽  
Three Dimensional ◽  
Simons Theory ◽  
Quantum Field ◽  
Topological Quantum ◽  
Chern Simons ◽  
Direct Implementation ◽  
Chern Simons Theory

A new, formal, noncombinatorial approach to invariants of three-dimensional manifolds of Reshetikhin, Turaev and Witten in the framework of nonperturbative topological quantum Chern–Simons theory, corresponding to an arbitrary compact simple Lie group, is presented. A direct implementation of surgery instructions in the context of quantum field theory is proposed. An explicit form of the specialization of the invariant to the group SU(2) is shown.

scholarly journals Fermi gas approach to general rank theories and quantum curves

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Naotaka Kubo
Keyword(s):  
Matrix Models ◽  
Critical Role ◽  
Three Dimensional ◽  
Fermi Gas ◽  
Fermi Gases ◽  
Partition Functions ◽  
Density Matrices ◽  
General Rank ◽  
Chern Simons ◽  
The Ideal

Abstract It is known that matrix models computing the partition functions of three-dimensional $$ \mathcal{N} $$ N = 4 superconformal Chern-Simons theories described by circular quiver diagrams can be written as the partition functions of ideal Fermi gases when all the nodes have equal ranks. We extend this approach to rank deformed theories. The resulting matrix models factorize into factors depending only on the relative ranks in addition to the Fermi gas factors. We find that this factorization plays a critical role in showing the equality of the partition functions of dual theories related by the Hanany-Witten transition. Furthermore, we show that the inverses of the density matrices of the ideal Fermi gases can be simplified and regarded as quantum curves as in the case without rank deformations. We also comment on four nodes theories using our results.

scholarly journals Cobalt-based magnetic Weyl semimetals with high-thermodynamic stabilities

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Wei Luo ◽  
Yuma Nakamura ◽  
Jinseon Park ◽  
Mina Yoon
Keyword(s):  
Tight Binding ◽  
Three Dimensional ◽  
Interlayer Coupling ◽  
First Principles Calculation ◽  
Optimization Approach ◽  
Binding Model ◽  
Nodal Lines ◽  
Weyl Semimetal ◽  
Topological Quantum ◽  
First Time

AbstractRecent experiments identified Co3Sn2S2 as the first magnetic Weyl semimetal (MWSM). Using first-principles calculation with a global optimization approach, we explore the structural stabilities and topological electronic properties of cobalt (Co)-based shandite and alloys, Co3MM’X2 (M/M’ = Ge, Sn, Pb, X = S, Se, Te), and identify stable structures with different Weyl phases. Using a tight-binding model, for the first time, we reveal that the physical origin of the nodal lines of a Co-based shandite structure is the interlayer coupling between Co atoms in different Kagome layers, while the number of Weyl points and their types are mainly governed by the interaction between Co and the metal atoms, Sn, Ge, and Pb. The Co3SnPbS2 alloy exhibits two distinguished topological phases, depending on the relative positions of the Sn and Pb atoms: a three-dimensional quantum anomalous Hall metal, and a MWSM phase with anomalous Hall conductivity (~1290 Ω−1 cm−1) that is larger than that of Co2Sn2S2. Our work reveals the physical mechanism of the origination of Weyl fermions in Co-based shandite structures and proposes topological quantum states with high thermal stability.

scholarly journals Wilson loop algebras and quantum K-theory for Grassmannians

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Hans Jockers ◽  
Peter Mayr ◽  
Urmi Ninad ◽  
Alexander Tabler
Keyword(s):  
Wilson Loop ◽  
Gauge Theories ◽  
Wilson Line ◽  
Quantum Cohomology ◽  
Three Dimensional ◽  
Loop Algebra ◽  
Loop Algebras ◽  
Verlinde Algebra ◽  
K Theory ◽  
Chern Simons

Abstract We study the algebra of Wilson line operators in three-dimensional $$ \mathcal{N} $$ N = 2 supersymmetric U(M ) gauge theories with a Higgs phase related to a complex Grassmannian Gr(M, N ), and its connection to K-theoretic Gromov-Witten invariants for Gr(M, N ). For different Chern-Simons levels, the Wilson loop algebra realizes either the quantum cohomology of Gr(M, N ), isomorphic to the Verlinde algebra for U(M ), or the quantum K-theoretic ring of Schubert structure sheaves studied by mathematicians, or closely related algebras.

scholarly journals DISCRETE AND CONTINUUM APPROACHES TO THREE-DIMENSIONAL QUANTUM GRAVITY

1991 ◽  
Vol 06 (39) ◽  
pp. 3591-3600 ◽  
Author(s):  
HIROSI OOGURI ◽  
NAOKI SASAKURA
Keyword(s):  
Gauge Theory ◽  
Moduli Space ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Analogue Model ◽  
Gauge Invariant ◽  
Invariant Functions ◽  
Dimensional Lattice ◽  
Chern Simons ◽  
Dimensional Surface

It is shown that, in the three-dimensional lattice gravity defined by Ponzano and Regge, the space of physical states is isomorphic to the space of gauge-invariant functions on the moduli space of flat SU(2) connections over a two-dimensional surface, which gives physical states in the ISO(3) Chern–Simons gauge theory. To prove this, we employ the q-analogue of this model defined by Turaev and Viro as a regularization to sum over states. A recent work by Turaev suggests that the q-analogue model itself may be related to an Euclidean gravity with a cosmological constant proportional to 1/k2, where q=e2πi/(k+2).

scholarly journals Three-dimensional Maxwellian extended Newtonian gravity and flat limit

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Patrick Concha ◽  
Lucrezia Ravera ◽  
Evelyn Rodríguez ◽  
Gustavo Rubio
Keyword(s):  
Cosmological Constant ◽  
Three Dimensional ◽  
Expansion Method ◽  
Gravity Models ◽  
Newtonian Gravity ◽  
Newtonian Theory ◽  
Relativistic Limit ◽  
Expansion Procedure ◽  
Three Space ◽  
Chern Simons

Abstract In the present work we find novel Newtonian gravity models in three space-time dimensions. We first present a Maxwellian version of the extended Newtonian gravity, which is obtained as the non-relativistic limit of a particular U(1)-enlargement of an enhanced Maxwell Chern-Simons gravity. We show that the extended Newtonian gravity appears as a particular sub-case. Then, the introduction of a cosmological constant to the Maxwellian extended Newtonian theory is also explored. To this purpose, we consider the non-relativistic limit of an enlarged symmetry. An alternative method to obtain our results is presented by applying the semigroup expansion method to the enhanced Nappi-Witten algebra. The advantages of considering the Lie algebra expansion procedure is also discussed.

Chern Numbers and Green's Functions in Solid State Physics

1997 ◽  
Vol 11 (11) ◽  
pp. 1389-1410
Author(s):  
Xiao-Rong Wu-Morrow ◽  
Cecile Dewitt-Morette ◽  
Lev Rozansky
Keyword(s):  
Periodic Potential ◽  
Solid State Physics ◽  
Hall Conductance ◽  
Energy Eigenvalues ◽  
Finite Dimensional ◽  
Topological Quantum ◽  
Chern Numbers ◽  
Density Response ◽  
Physical Quantities ◽  
Noninteracting Electron

Using the energy Green's function formulation proposed by Niu 1 for particle densities, we construct and clarify the nature of the topological invariant assigned to the Hall conductance in the Hall system of 2-dimensional noninteracting electron gas; we identify this topological quantum number explicitly as the first Chern number of a complex vector bundle over a 2-torus parametrized by the magnetic potential (a1, a2); the fibres are finite dimensional spaces spanned by eigenfunctions of the system with energy eigenvalues below the Fermi energy. Other cases can be treated by a similar procedure, namely, by recognizing that some physical quantities are integrals of curvatures defined on a nontrivial finite dimensional complex bundle. Therefore, in suitable units, they take integer values. We treat, as an example, the electron density response to a dilation of a periodic potential. The integer in this case is the number of Bloch bands. The quantization of the Hall conductance and density response is also shown in the presence of disorder.

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