Inequalities for Wilson loops, cusp singularities, area law and shape of a drum

P. V. Pobylitsa

Home/Archive/arXiv

arXiv · hep-th/0702123

Inequalities for Wilson loops, cusp singularities, area law and shape of a drum

P. V. Pobylitsa

View original source ↗Read source document ↗Export metadata ↓

Abstract

Inequalities are derived for Wilson loops generalizing the well-known Bachas inequality for rectangular contours. The inequalities are compatible with the area law for large contours. The Polyakov cusp anomalous dimension of Wilson lines (playing an important role in QCD applications to hard processes) has a convex angular dependence. This convexity is crucial for the consistency of the inequalities with renormalization. Some parallel properties can be found in the string theory. The Kac-Ray cusp term from the "shape of a drum" problem has the same angular convexity property and plays the role of the cusp anomalous dimension in the effective string model for Wilson loops studied by Luescher, Symanzik and Weisz (LSW). Using heuristic arguments based on the LSW model, one can find an interesting connection between the inequalities for Wilson loops and inequalities for determinants of two-dimensional Laplacians with Dirichlet boundary conditions on the closed contours associated with Wilson loops.

Explore related subjects

hep-th hep-lat hep-ph

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

P. V. Pobylitsa. 2007-02-15. Inequalities for Wilson loops, cusp singularities, area law and shape of a drum. https://arxiv.org/abs/hep-th/0702123

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Localisation of $\mathcal{N} = (2,2)$ theories on spindles of both twists

We consider two-dimensional $\mathcal{N}=(2,2)$ supersymmetric field theories living on a spindle $\mathbb{WCP}_{[n_1,n_2]}^1$. Starting from the spindle solutions of five-dimensional STU gauged supergravity, we construct theories on a spindle which preserve supersymmetry via either the twist or anti-twist mechanism and admit two Killing spinors of opposite R-charge. While the study of field theories on anti-twisted spindles has already been undertaken in some detail, the advantage of our approach allows for the derivation of analogous results in the twist case. We apply the technique of supersymmetric localisation to compute the exact partition function for a theory consisting of an abelian vector multiplet and a charged chiral multiplet in the presence of a Fayet-Iliopoulos term. We compare and contrast the results for the twisted and anti-twisted spindle and find a general formula which encompasses the partition function for both cases simultaneously.

hep-th↗

arXiv2026

Some universalities in the partition functions of low-dimensional gravity models

In this work, first, we discuss the connections between various low-dimensional quantum gravity models, including 3d Chern-Simons, 2d Jackiw-Teitelboim (JT), 2d background field (BF) theory, 2d Liouville, 2d Wess-Zumino-Witten (WZW), and 1d Schwarzian, which are related through holography and dimension reduction, and discuss some universalities in their partition functions. Then, we specifically examine the JT partition function and the partition function of $\mathcal{N}=(2,2)$ on $S^2$ and $\text{AdS}_2$ and discuss their similarities and therefore examine our proposed universalities. We change the parameters in each model and based on the change in the structure of the partition functions, strengthen our conjectures. We also use eigenfunctions, spectra and the behaviors of Wheeler-DeWitt wavefunctions to generate more universalities between these low-dimensional quantum gravity models, specifically in their partition functions. Finally, we use entanglement entropy, complexity and RG flows, particularly in the context of wormholes, to find more universalities in quantum gravity models.

hep-th↗

arXiv2026

A Note on a High-Energy Limit of Gravitational Perturbation Theory

The post-Minkowskian expansion of general relativity expands the metric in Newton's constant G around flat space-time, but much effort currently focuses on ways to extend its range of applicability by summing the perturbative series to all orders. A regime of particular interest is a specific high-energy limit where a formula derived recently provides the momentum kick of binary scattering problem to all orders, and even suggests an approach towards strong coupling. We show that this is an asymptotic expansion. Although the series diverges we give evidence that it is Borel summable, and the full function in integral form is finite. As a by-product we determine the transcendentality properties of the coefficients in the expanded expression.

hep-th↗