首页/论文/2007.05968

arXiv 2007.059682020-07-12hep-thhep-lat

$\mathbb{1}$-Loop Theory

Alexander S. Glasser, Hong Qin

备注：: 10 pages, 3 figures

英文摘要：

A new formalism for lattice gauge theory is developed that preserves Poincaré symmetry in a discrete universe. We define the $\mathbb{1}$-loop, a generalization of the Wilson loop that reformulates classical differential equations of motion as identity-valued multiplicative loops of Lie group elements of the form ${[g_1\cdots g_n]=\mathbb{1}}$. A lattice Poincaré gauge theory of gravity is thus derived that employs a novel matter field construction and recovers Einstein's vacuum equations in the appropriate limit.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

Super-Poincare Covariant Two-Loop Superstring Amplitudes

The super-Poincare covariant formalism for the superstring is used to compute massless four-point two-loop amplitudes in ten-dimensional superspace. The computations are much simpler than in the RNS formalism and include both external bosons and fermions.

2005-03-25hep-th

Super-de Sitter and alternative super-Poincaré symmetries

It is well-known that de Sitter Lie algebra $\mathfrak{o}(1,4)$ contrary to anti-de Sitter one $\mathfrak{o}(2,3)$ does not have a standard $\mathbb{Z}_2$-graded superextension. We show here that the Lie algebra $\mathfrak{o}(1,4)$ has a superextension based on the $\mathbb{Z}_2\times\mathbb{Z}_2$-grading. Using the standard contraction procedure for this superextension we obtain an {\it alternative} super-Poincaré algebra with the $\mathbb{Z}_2\times\mathbb{Z}_2$-grading.

2016-10-05hep-th

$κ$-Poincaré invariant orientable field theories at 1-loop

We consider a family of $κ$-Poincaré invariant scalar field theories on 4-d $κ$-Minkowski space with quartic orientable interaction, that is for which $ϕ$ and its conjugate $ϕ^†$ alternate in the quartic interaction, and whose kinetic operator is the square of a $U_κ(iso(4))$-equivariant Dirac operator. The formal commutative limit yields the standard complex $ϕ^4$ theory. We find that the 2-point function receives UV linearly diverging 1-loop corrections while it stays free of IR singularities that would signal occurrence of UV/IR mixing. We find that all the 1-loop planar and non-planar cont…

2019-01-07hep-thmath-phmath.MP

$\mathrm{D=10}$ Super-Yang-Mills Theory and Poincaré Duality in Supermanifolds

We consider super Yang-Mills theory on supermanifolds $\mathcal{M}^{(D|m)}$ using integral forms. The latter are used to define a geometric theory of integration and are essential for a consistent action principle. The construction relies on Picture Changing Operators $\mathbb{Y}^{(0|m)}$, analogous to those introduced in String Theory, that admit the geometric interpretation of Poincaré duals of closed submanifolds of superspace $\mathcal{S}^{(D|0)} \subset \mathcal{M}^{(D|m)}$ having maximal bosonic dimension $D$. We discuss the case of Super-Yang-Mills theory in $D=10$ with $\mathcal{N}=1$ …

2017-10-31hep-th

Physical meaning and consequences of the loop IR divergences in global dS

Following arXiv:1012.2107 we show that in global de Sitter space its isometry is broken by the loop IR divergences for any invariant vacuum state of the massive scalars. We derive kinetic equation in global de Sitter space. It follows from the Dyson-Schwinger equation of the Schwinger-Keldysh diagrammatic technique in IR limit and allows to understand the physical meaning and consequences of the loop IR divergences. In many respects the isometry breaking in global dS is similar to the one in the contracting Poincare patch of de Sitter space. Hence, as a warm up exercise we study the kinetic eq…

2013-02-11hep-th

Modular graph functions and odd cuspidal functions -- Fourier and Poincaré series

Modular graph functions are $SL(2,{\mathbb Z})$-invariant functions associated with Feynman graphs of a two-dimensional conformal field theory on a torus of modulus $τ$. For one-loop graphs they reduce to real analytic Eisenstein series. We obtain the Fourier series, including the constant and non-constant Fourier modes, of all two-loop modular graph functions, as well as their Poincaré series with respect to $Γ_\infty \backslash PSL(2,{\mathbb Z})$. The Fourier and Poincaré series provide the tools to compute the Petersson inner product of two-loop modular graph functions using Rankin-Selberg…

2021-02-05hep-thmath.NT

更多相关论文收起更多论文

UV/IR mixing as a twisted Poincaré anomaly

We analyze symmetries of the 1-loop effective action of ϕ^4 noncommutative field theory. It is shown, that despite the twisted Poincaré invariance of the classical noncommutative action, its 1-loop quantum counterpart lacks this invariance. Though Noether analysis of the model is somewhat obscure, it is still possible to interpret this symmetry breaking as a quantum anomaly due to inappropriate choice of the quantization method.

2012-10-31hep-thmath-phmath.MP

IR divergences and kinetic equation in de Sitter space. (Poincare patch; Principal series)

We explicitly show that the one loop IR correction to the two--point function in de Sitter space scalar QFT does not reduce just to the mass renormalization. The proper interpretation of the loop corrections is via particle creation revealing itself through the generation of the quantum averages $<a^+_p a_p>$, $<a_p a_{-p}>$ and $<a^+_p a^+_{-p}>$, which slowly change in time. We show that this observation in particular means that loop corrections to correlation functions in de Sitter space can not be obtained via analytical continuation of those calculated on the sphere. We find harmonics for…

2013-01-14gr-qchep-th

迈向具有传播挠率的微扰单模庞加莱规范理论

Towards Perturbative Unimodular Poincaré Gauge Theories with Propagating Torsion

Universidade do Estado do Rio de Janeiro（里约热内卢州立大学）；Universidade Federal Fluminense（弗鲁米嫩塞联邦大学）；University of Graz（格拉茨大学）

该研究探讨具有传播挠率的庞加莱引力规范理论与其单模对应理论的单圈关系，发现特定背景下单模约束不改变局域单圈挠率动力学，并指出等价性的局限及扩展方向。

2026-08-25gr-qchep-th

On the quantum structure of spacetime and its relation to the quantum theory of fields: $κ$-Poincaré invariant field theories and other examples

The dissertation deals with noncommutative field theories, namely field theories compatible with the existence of a minimal (quantum gravity) length scale. Two families of quantum spacetime are considered. One is characterized by semisimple Lie algebras of coordinates. The other is characterized by solvable Lie algebras. The explicit construction of corresponding Weyl-like star products is given. We then focus on two specific examples of quantum space and study the quantum properties of various models of scalar field theory with quartic interactions built on them. The corresponding 2-point and…

2018-11-15hep-thmath-phmath.MP

Poincaré and sl(2) algebras of order 3

In this paper we initiate a general classification for Lie algebras of order 3 and we give all Lie algebras of order 3 based on $\mathfrak{sl}(2,\mathbb C)$ and $\mathfrak{iso}(1,3)$ the Poincaré algebra in four-dimensions. We then set the basis of the theory of the deformations (in the Gerstenhaber sense) and contractions for Lie algebras of order 3.

2007-10-29hep-thmath-phmath.MP

$D^6R^4$ curvature corrections, modular graph functions and Poincaré series

In this note we study the U-duality invariant coefficient functions of higher curvature corrections to the four-graviton scattering amplitude in type IIB string theory compactified on a torus. The main focus is on the $D^6R^4$ term that is known to satisfy an inhomogeneous Laplace equation. We exhibit a novel method for solving this equation in terms of a Poincaré series ansatz and recover known results in $D=10$ dimensions and find new results in $D<10$ dimensions. We also apply the method to modular graph functions as they arise from closed superstring one-loop amplitudes.

2018-03-27hep-thmath.NT