scholarly journals Small Gauge Transformations and Universal Geometry in Heterotic Theories

2020 ◽  
Author(s):  
Jock McOrist ◽  
◽  
Roberto Sisca ◽  
Keyword(s):  
Moduli Space ◽  
Deformation Theory ◽  
Bianchi Identity ◽  
Gauge Transformations ◽  
Gauge Fixing ◽  
Order Deformation ◽  
Small Gauge ◽  
Universal Bundle ◽  
Universal Geometry ◽  
Lee Form

The first part of this paper describes in detail the action of small gauge transformations in heterotic supergravity. We show a convenient gauge fixing is 'holomorphic gauge' together with a condition on the holomorphic top form. This gauge fixing, combined with supersymmetry and the Bianchi identity, allows us to determine a set of non-linear PDEs for the terms in the Hodge decomposition. Although solving these in general is highly non-trivial, we give a prescription for their solution perturbatively in α and apply this to the moduli space metric. The second part of this paper relates small gauge transformations to a choice of connection on the moduli space. We show holomorphic gauge is related to a choice of holomorphic structure and Lee form on a 'universal bundle'. Connections on the moduli space have field strengths that appear in the second order deformation theory and we point out it is generically the case that higher order deformations do not commute.

Gravitation Theory in Path Space

1997 ◽  
Vol 52 (1-2) ◽  
pp. 86-96
Author(s):  
Claudio Teitelboim
Keyword(s):  
Bianchi Identity ◽  
Riemann Tensor ◽  
Functional Integral ◽  
Path Space ◽  
Gravitation Theory ◽  
Antisymmetric Part ◽  
Gauge Transformations ◽  
Gauge Fixing ◽  
The Continuum

Abstract A formulation of gravitation theory originally proposed by Mandelstam is re-examined. The idea is to avoid the use of coordinates while staying in the continuum. This is accomplished by regarding a point as the end of a path. The theory is then formulated in the space of all paths. The analysis relies on the properties of path deformations. These deformations play the role of gauge transformations in path space. Their algebra is established. It closes if and only if the defining conditions of a riemannian geometry hold (Bianchi identity and vanishing of the antisymmetric part of the Riemann tensor in three of its indices). Two problems faced by Mandelstam are solved: (i) An explicit formula is given which establishes when two neighboring paths end at the same point, (ii) An action principle is given, in terms of a functional integral over path space. It is also indicated how to reconstruct the metric from the curvature through gauge fixing in path space. Brief comments are offered on the possibility of developing an invariant description of loops regarded as boundaries of two-dimensional surfaces.

scholarly journals Extracting topological information from momentum space propagators

2019 ◽  
Vol 79 (10) ◽  
Author(s):  
Fabrizio Canfora ◽  
David Dudal ◽  
Alex Giacomini ◽  
Igor F. Justo ◽  
Pablo Pais ◽  
...  
Keyword(s):  
Gauge Invariance ◽  
Momentum Space ◽  
Chiral Symmetry Breaking ◽  
Topological Invariant ◽  
Analytic Structure ◽  
Topological Information ◽  
Gauge Transformations ◽  
Small Gauge ◽  
Topological Number

Abstract A new topological invariant quantity, sensitive to the analytic structure of both fermionic and bosonic propagators, is proposed. The gauge invariance of our construct is guaranteed for at least small gauge transformations. A generalization compatible with the presence of complex poles is introduced and applied to the classification of propagators typically emerging from non-perturbative considerations. We present partial evidence that the topological number can be used to detect chiral symmetry breaking or deconfinement.

VERSAL DEFORMATIONS OF THREE-DIMENSIONAL LIE ALGEBRAS AS L∞ ALGEBRAS

2005 ◽  
Vol 07 (02) ◽  
pp. 145-165 ◽  
Author(s):  
ALICE FIALOWSKI ◽  
MICHAEL PENKAVA
Keyword(s):  
Vector Space ◽  
Lie Algebras ◽  
Moduli Space ◽  
Deformation Theory ◽  
Three Dimensional ◽  
3 Dimensional ◽  
Exterior Degree ◽  
Versal Deformations

We consider versal deformations of 0|3-dimensional L∞ algebras, also called strongly homotopy Lie algebras, which correspond precisely to ordinary (non-graded) three-dimensional Lie algebras. The classification of such algebras is well-known, although we shall give a derivation of this classification using an approach of treating them as L∞ algebras. Because the symmetric algebra of a three-dimensional odd vector space contains terms only of exterior degree less than or equal to three, the construction of versal deformations can be carried out completely. We give a characterization of the moduli space of Lie algebras using deformation theory as a guide to understanding the picture.

A boundary divisor in the moduli spaces of stable quintic surfaces

2017 ◽  
Vol 28 (04) ◽  
pp. 1750021 ◽  
Author(s):  
Julie Rana
Keyword(s):  
Algebraic Geometry ◽  
Moduli Space ◽  
Moduli Spaces ◽  
Deformation Theory ◽  
General Type ◽  
Topological Invariants ◽  
Surfaces Of General Type ◽  
Wide Range ◽  
Stable Surfaces ◽  
Standing Question

We give a bound on which singularities may appear on Kollár–Shepherd-Barron–Alexeev stable surfaces for a wide range of topological invariants and use this result to describe all stable numerical quintic surfaces (KSBA-stable surfaces with [Formula: see text]) whose unique non-Du Val singularity is a Wahl singularity. We then extend the deformation theory of Horikawa to the log setting in order to describe the boundary divisor of the moduli space [Formula: see text] corresponding to these surfaces. Quintic surfaces are the simplest examples of surfaces of general type and the question of describing their moduli is a long-standing question in algebraic geometry.

Buckling of Composite Laminates Using Higher Order Deformation Theory

2004 ◽  
Author(s):  
N. G. R. Iyengar ◽  
Arindam Chakraborty
Keyword(s):  
Transverse Shear ◽  
Composite Laminates ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Higher Order ◽  
Shear Loading ◽  
Side Ratio ◽  
Order Deformation ◽  
Shear Effects ◽  
Transverse Shear Effects

Response of composite laminates under in-plane compressive or shear loadings is of interest to the analyst and designers. Since they are thin, they are prone to instability under in-plane loads. Transverse shear effects are important even for thin laminates since elastic modulus and shear modulus are independent properties. For very thick laminates neglecting transverse shear effects leads to completely erroneous results. A number of different theories have been suggested by different investigators to account for transverse shear effects. In this investigation, an attempt has been made to take into account transverse shear effects for the stability analysis of moderately thick/very thick composite laminates under in-plane compressive and shear loading using a “SIMPLE HIGHER ORDER SHEAR DEFORMATION THEORY” based on four unknown displacements instead of five which is commonly used for most of the other higher order theories. A C1 continuous shear flexible finite element based on the proposed HSDT is developed using the Hermite cubic rectangular element. The analytical results obtained have been compared with the available results in literature. Effect of various parameters like aspect ratio, thickness to side ratio, fiber orientation and material properties have been studied in detail.

scholarly journals THE PENROSE LIMIT OF AdS×S SPACE AND HOLOGRAPHY

2004 ◽  
Vol 19 (12) ◽  
pp. 887-895
Author(s):  
GEORGE SIOPSIS
Keyword(s):  
Heisenberg Algebra ◽  
Killing Vectors ◽  
Gauge Transformations ◽  
Gauge Fixing ◽  
Holographic Screen ◽  
Penrose Limit

In the Penrose limit, AdS ×S space turns into a Cahen–Wallach (CW) space whose Killing vectors satisfy a Heisenberg algebra. This algebra is mapped onto the holographic screen on the boundary of AdS. We show that the Heisenberg algebra on the boundary of AdS may be obtained directly from the CW space by appropriately constraining the states defined on it. The transformations generated by the constraint are similar to gauge transformations. The "holographic screen" on the CW space is thus obtained as a "gauge-fixing" condition.

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