Renormalization and mixing of staple-shaped Wilson line operators on the lattice revisited

Abstract Correlators of Wilson-line operators in non-abelian gauge theories are known to exponentiate, and their logarithms can be organised in terms of collections of Feynman diagrams called webs. In [1] we introduced the concept of Cweb, or correlator web, which is a set of skeleton diagrams built with connected gluon correlators, and we computed the mixing matrices for all Cwebs connecting four or five Wilson lines at four loops. Here we complete the evaluation of four-loop mixing matrices, presenting the results for all Cwebs connecting two and three Wilson lines. We observe that the conjuctured column sum rule is obeyed by all the mixing matrices that appear at four-loops. We also show how low-dimensional mixing matrices can be uniquely determined from their known combinatorial properties, and provide some all-order results for selected classes of mixing matrices. Our results complete the required colour building blocks for the calculation of the soft anomalous dimension matrix at four-loop order.

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Dressing bulk fields in AdS3

Journal of High Energy Physics ◽

10.1007/jhep10(2020)189 ◽

2020 ◽

Vol 2020 (10) ◽

Author(s):

Daniel Kabat ◽

Gilad Lifschytz

Keyword(s):

Scalar Field ◽

Wilson Line ◽

Bulk Scalar Field

Abstract We study a set of CFT operators suitable for reconstructing a charged bulk scalar field ϕ in AdS3 (dual to an operator $$ \mathcal{O} $$ O of dimension ∆ in the CFT) in the presence of a conserved spin-n current in the CFT. One has to sum a tower of smeared non-primary scalars $$ {\partial}_{+}^m{J}^{(m)} $$ ∂ + m J m , where J(m) are primaries with twist ∆ and spin m built from $$ \mathcal{O} $$ O and the current. The coefficients of these operators can be fixed by demanding that bulk correlators are well-defined: with a simple ansatz this requirement allows us to calculate bulk correlators directly from the CFT. They are built from specific polynomials of the kinematic invariants up to a freedom to make field redefinitions. To order 1/N this procedure captures the dressing of the bulk scalar field by a radial generalized Wilson line.

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Symmetry-resolved entanglement in AdS3/CFT2 coupled to U(1) Chern-Simons theory

Journal of High Energy Physics ◽

10.1007/jhep07(2021)030 ◽

2021 ◽

Vol 2021 (7) ◽

Author(s):

Suting Zhao ◽

Christian Northe ◽

René Meyer

Keyword(s):

Field Theory ◽

Conformal Field Theory ◽

Gauge Field ◽

Wilson Line ◽

Entanglement Entropy ◽

Simons Theory ◽

Two Dimensional ◽

Conformal Field ◽

Chern Simons ◽

Chern Simons Theory

Abstract We consider symmetry-resolved entanglement entropy in AdS3/CFT2 coupled to U(1) Chern-Simons theory. We identify the holographic dual of the charged moments in the two-dimensional conformal field theory as a charged Wilson line in the bulk of AdS3, namely the Ryu-Takayanagi geodesic minimally coupled to the U(1) Chern-Simons gauge field. We identify the holonomy around the Wilson line as the Aharonov-Bohm phases which, in the two-dimensional field theory, are generated by charged U(1) vertex operators inserted at the endpoints of the entangling interval. Furthermore, we devise a new method to calculate the symmetry resolved entanglement entropy by relating the generating function for the charged moments to the amount of charge in the entangling subregion. We calculate the subregion charge from the U(1) Chern-Simons gauge field sourced by the bulk Wilson line. We use our method to derive the symmetry-resolved entanglement entropy for Poincaré patch and global AdS3, as well as for the conical defect geometries. In all three cases, the symmetry resolved entanglement entropy is determined by the length of the Ryu-Takayanagi geodesic and the Chern-Simons level k, and fulfills equipartition of entanglement. The asymptotic symmetry algebra of the bulk theory is of $$ \hat{\mathfrak{u}}{(1)}_k $$ u ̂ 1 k Kac-Moody type. Employing the $$ \hat{\mathfrak{u}}{(1)}_k $$ u ̂ 1 k Kac-Moody symmetry, we confirm our holographic results by a calculation in the dual conformal field theory.

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Supersymmetric solitons and a degeneracy of solutions in AdS/CFT

Journal of High Energy Physics ◽

10.1007/jhep07(2021)015 ◽

2021 ◽

Vol 2021 (7) ◽

Author(s):

Andrés Anabalón ◽

Simon F. Ross

Keyword(s):

Phase Transition ◽

Riemann Surface ◽

Magnetic Flux ◽

Gauge Field ◽

Wilson Line ◽

Saddle Points ◽

Planar Boundary ◽

Four Dimensions ◽

Special Value

Abstract We study Lorentzian supersymmetric configurations in D = 4 and D = 5 gauged $$ \mathcal{N} $$ N = 2 supergravity. We show that there are smooth 1/2 BPS solutions which are asymptotically AdS4 and AdS5 with a planar boundary, a compact spacelike direction and with a Wilson line on that circle. There are solitons where the S1 shrinks smoothly to zero in the interior, with a magnetic flux through the circle determined by the Wilson line, which are AdS analogues of the Melvin fluxtube. There is also a solution with a constant gauge field, which is pure AdS. Both solutions preserve half of the supersymmetries at a special value of the Wilson line. There is a phase transition between these two saddle-points as a function of the Wilson line precisely at the supersymmetric point. Thus, the supersymmetric solutions are degenerate, at least at the supergravity level. We extend this discussion to one of the Romans solutions in four dimensions when the Euclidean boundary is S1× Σg where Σg is a Riemann surface with genus g > 0. We speculate that the supersymmetric state of the CFT on the boundary is dual to a superposition of the two degenerate geometries.

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A path integral formulation for particle detectors: the Unruh-DeWitt model as a line defect

Journal of High Energy Physics ◽

10.1007/jhep03(2021)076 ◽

2021 ◽

Vol 2021 (3) ◽

Author(s):

Ivan M. Burbano ◽

T. Rick Perche ◽

Bruno de S. L. Torres

Keyword(s):

Path Integral ◽

Degrees Of Freedom ◽

Wilson Line ◽

Transition Probability ◽

Relativistic Quantum ◽

Quantum Fields ◽

Line Defect ◽

Particle Detectors ◽

Nonlocal Operators ◽

Detector Model

Abstract Particle detectors are an ubiquitous tool for probing quantum fields in the context of relativistic quantum information (RQI). We formulate the Unruh-DeWitt (UDW) particle detector model in terms of the path integral formalism. The formulation is able to recover the results of the model in general globally hyperbolic spacetimes and for arbitrary detector trajectories. Integrating out the detector’s degrees of freedom yields a line defect that allows one to express the transition probability in terms of Feynman diagrams. Inspired by the light-matter interaction, we propose a gauge invariant detector model whose associated line defect is related to the derivative of a Wilson line. This is another instance where nonlocal operators in gauge theories can be interpreted as physical probes for quantum fields.

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Wilson loop algebras and quantum K-theory for Grassmannians

Journal of High Energy Physics ◽

10.1007/jhep10(2020)036 ◽

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.

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Boundary electromagnetic duality from homological edge modes

Journal of High Energy Physics ◽

10.1007/jhep07(2021)192 ◽

2021 ◽

Vol 2021 (7) ◽

Author(s):

Philippe Mathieu ◽

Nicholas Teh

Keyword(s):

Gauge Theory ◽

Symplectic Structure ◽

Central Charge ◽

Wilson Line ◽

Boundary Term ◽

Global Symmetry ◽

Homotopy Pullback ◽

Line Singularities ◽

Topological Boundary

Abstract Recent years have seen a renewed interest in using ‘edge modes’ to extend the pre-symplectic structure of gauge theory on manifolds with boundaries. Here we further the investigation undertaken in [1] by using the formalism of homotopy pullback and Deligne- Beilinson cohomology to describe an electromagnetic (EM) duality on the boundary of M = B3 × ℝ. Upon breaking a generalized global symmetry, the duality is implemented by a BF-like topological boundary term. We then introduce Wilson line singularities on ∂M and show that these induce the existence of dual edge modes, which we identify as connections over a (−1)-gerbe. We derive the pre-symplectic structure that yields the central charge in [1] and show that the central charge is related to a non-trivial class of the (−1)-gerbe.

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Holographic entanglement entropy of the Coulomb branch

Journal of High Energy Physics ◽

10.1007/jhep04(2021)153 ◽

2021 ◽

Vol 2021 (4) ◽

Author(s):

Adam Chalabi ◽

S. Prem Kumar ◽

Andy O’Bannon ◽

Anton Pribytok ◽

Ronnie Rodgers ◽

...

Keyword(s):

W Boson ◽

Wilson Line ◽

Entanglement Entropy ◽

Physical Principle ◽

Boson Mass ◽

Extremal Black Hole ◽

Energy Tensor ◽

Large Radius ◽

Coulomb Branch ◽

Yang Mills

Abstract We compute entanglement entropy (EE) of a spherical region in (3 + 1)-dimensional $$ \mathcal{N} $$ N = 4 supersymmetric SU(N) Yang-Mills theory in states described holographically by probe D3-branes in AdS5 × S5. We do so by generalising methods for computing EE from a probe brane action without having to determine the probe’s backreaction. On the Coulomb branch with SU(N) broken to SU(N − 1) × U(1), we find the EE monotonically decreases as the sphere’s radius increases, consistent with the a-theorem. The EE of a symmetric-representation Wilson line screened in SU(N − 1) also monotonically decreases, although no known physical principle requires this. A spherical soliton separating SU(N) inside from SU(N − 1) × U(1) outside had been proposed to model an extremal black hole. However, we find the EE of a sphere at the soliton’s radius does not scale with the surface area. For both the screened Wilson line and soliton, the EE at large radius is described by a position-dependent W-boson mass as a short-distance cutoff. Our holographic results for EE and one-point functions of the Lagrangian and stress-energy tensor show that at large distance the soliton looks like a Wilson line in a direct product of fundamental representations.

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Heterotic line bundle models on generalized complete intersection Calabi Yau manifolds

Journal of High Energy Physics ◽

10.1007/jhep05(2021)105 ◽

2021 ◽

Vol 2021 (5) ◽

Author(s):

Magdalena Larfors ◽

Davide Passaro ◽

Robin Schneider

Keyword(s):

Line Bundle ◽

Complete Intersection ◽

Particle Physics ◽

Model Building ◽

Wilson Line ◽

Symmetry Groups ◽

The Standard Model ◽

Order Of Magnitude ◽

Systematic Program ◽

Calabi Yau Manifolds

Abstract The systematic program of heterotic line bundle model building has resulted in a wealth of standard-like models (SLM) for particle physics. In this paper, we continue this work in the setting of generalised Complete Intersection Calabi Yau (gCICY) manifolds. Using the gCICYs constructed in ref. [1], we identify two geometries that, when combined with line bundle sums, are directly suitable for heterotic GUT models. We then show that these gCICYs admit freely acting ℤ2 symmetry groups, and are thus amenable to Wilson line breaking of the GUT gauge group to that of the standard model. We proceed to a systematic scan over line bundle sums over these geometries, that result in 99 and 33 SLMs, respectively. For the first class of models, our results may be compared to line bundle models on homotopically equivalent Complete Intersection Calabi Yau manifolds. This shows that the number of realistic configurations is of the same order of magnitude.

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The non-perturbative QCD Debye mass from a Wilson line operator

Physics Letters B ◽

10.1016/s0370-2693(99)00641-3 ◽

1999 ◽

Vol 459 (1-3) ◽

pp. 259-264 ◽

Cited By ~ 41

Author(s):

M. Laine ◽

O. Philipsen

Keyword(s):

Perturbative Qcd ◽

Wilson Line ◽

Debye Mass ◽

Line Operator

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