Search results for "loop"
showing 10 items of 608 documents
Wilson Loop Form Factors: A New Duality
2017
We find a new duality for form factors of lightlike Wilson loops in planar $\mathcal N=4$ super-Yang-Mills theory. The duality maps a form factor involving an $n$-sided lightlike polygonal super-Wilson loop together with $m$ external on-shell states, to the same type of object but with the edges of the Wilson loop and the external states swapping roles. This relation can essentially be seen graphically in Lorentz harmonic chiral (LHC) superspace where it is equivalent to planar graph duality. However there are some crucial subtleties with the cancellation of spurious poles due to the gauge fixing. They are resolved by finding the correct formulation of the Wilson loop and by careful analyti…
U(N) tools for loop quantum gravity: the return of the spinor
2011
We explore the classical setting for the U(N) framework for SU(2) intertwiners for loop quantum gravity (LQG) and describe the corresponding phase space in terms of spinors with appropriate constraints. We show how its quantization leads back to the standard Hilbert space of intertwiner states defined as holomorphic functionals. We then explain how to glue these intertwiners states in order to construct spin network states as wave-functions on the spinor phase space. In particular, we translate the usual loop gravity holonomy observables to our classical framework. Finally, we propose how to derive our phase space structure from an action principle which induces non-trivial dynamics for the…
Computing black hole entropy in loop quantum gravity from a conformal field theory perspective
2009
Motivated by the analogy proposed by Witten between Chern-Simons and conformal field theories, we explore an alternative way of computing the entropy of a black hole starting from the isolated horizon framework in loop quantum gravity. The consistency of the result opens a window for the interplay between conformal field theory and the description of black holes in loop quantum gravity.
Differential equations for loop integrals in Baikov representation
2018
We present a proof that differential equations for Feynman loop integrals can always be derived in Baikov representation without involving dimension-shift identities. We moreover show that in a large class of two- and three-loop diagrams it is possible to avoid squared propagators in the intermediate steps of setting up the differential equations.
One-loop effective action for a generic 2d dilaton gravity theory
1997
We study the one-loop effective action for a generic two-dimensional dilaton gravity theory conformally coupled to $N$ matter fields. We obtain an explicit expression for the effective action in the weak-coupling limit under a suitable restriction of the dilaton potential asymptotics. Our result applies to the CGHS model as well as to the spherically symmetric general relativity. The effective action is obtained by using the background-field method, and we take into account the loop contributions from all the fields in the classical action and from the ghosts. In the large-$N$ limit, and after an appropriate field redefinition, the one-loop correction takes the form of the Polyakov-Liouvill…
Coordinate space calculation of two- and three-loop sunrise-type diagrams, elliptic functions and truncated Bessel integral identities
2019
We integrate three-loop sunrise-type vacuum diagrams in $D_0=4$ dimensions with four different masses using configuration space techniques. The finite parts of our results are in numerical agreement with corresponding three-loop calculations in momentum space. Using some of the closed form results of the momentum space calculation we arrive at new integral identities involving truncated integrals of products of Bessel functions. For the non-degenerate finite two-loop sunrise-type vacuum diagram in $D_0=2$ dimensions we make use of the known closed form $p$-space result to express the moment of a product of three Bessel functions in terms of a sum of Claussen polylogarithms. Using results fo…
Fixed points of nonlinear sigma models in d>2
2009
Using Wilsonian methods, we study the renormalization group flow of the Nonlinear Sigma Model in any dimension $d$, restricting our attention to terms with two derivatives. At one loop we always find a Ricci flow. When symmetries completely fix the internal metric, we compute the beta function of the single remaining coupling, without any further approximation. For $d>2$ and positive curvature, there is a nontrivial fixed point, which could be used to define an ultraviolet limit, in spite of the perturbative nonrenormalizability of the theory. Potential applications are briefly mentioned.
Quantum geometry and microscopic black hole entropy
2006
9 pages, 6 figures.-- PACS nrs.: 04.60.Pp, 04.70.Dy.-- ISI Article Identifier: 000242448900013.-- Published online on Nov 28, 2006.
Integrands of loop amplitudes within loop-tree duality
2020
Using loop-tree duality, we relate a renormalised $n$-point $l$-loop amplitude in a quantum field theory to a phase-space integral of a regularised $l$-fold forward limit of a UV-subtracted $(n+2l)$-point tree-amplitude-like object. We show that up to three loops the latter object is easily computable from recurrence relations. This defines an integrand of the loop amplitude with a global definition of the loop momenta. Field and mass renormalisation are performed in the on-shell scheme.
Feynman integrals and iterated integrals of modular forms
2017
In this paper we show that certain Feynman integrals can be expressed as linear combinations of iterated integrals of modular forms to all orders in the dimensional regularisation parameter $\varepsilon$ . We discuss explicitly the equal mass sunrise integral and the kite integral. For both cases we give the alphabet of letters occurring in the iterated integrals. For the sunrise integral we present a compact formula, expressing this integral to all orders in $\varepsilon$ as iterated integrals of modular forms.