scholarly journals Exploring the landscape of CHL strings on Td

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Anamaría Font ◽  
Bernardo Fraiman ◽  
Mariana Graña ◽  
Carmen A. Núñez ◽  
Héctor Parra De Freitas
Keyword(s):  
Gauge Group ◽  
Moduli Space ◽  
Dynkin Diagram ◽  
Fundamental Groups ◽  
Computer Algorithms ◽  
Abelian Gauge ◽  
Reduced Rank ◽  
Systematic Exploration ◽  
String Models ◽  
Simply Connected

Abstract Compactifications of the heterotic string on special Td/ℤ2 orbifolds realize a landscape of string models with 16 supercharges and a gauge group on the left-moving sector of reduced rank d + 8. The momenta of untwisted and twisted states span a lattice known as the Mikhailov lattice II(d), which is not self-dual for d > 1. By using computer algorithms which exploit the properties of lattice embeddings, we perform a systematic exploration of the moduli space for d ≤ 2, and give a list of maximally enhanced points where the U(1)d+8 enhances to a rank d + 8 non-Abelian gauge group. For d = 1, these groups are simply-laced and simply-connected, and in fact can be obtained from the Dynkin diagram of E10. For d = 2 there are also symplectic and doubly-connected groups. For the latter we find the precise form of their fundamental groups from embeddings of lattices into the dual of II(2). Our results easily generalize to d > 2.

NEW POLARIZATIONS ON THE MODULI SPACES AND THE THURSTON COMPACTIFICATION OF TEICHMÜLLER SPACE

1998 ◽  
Vol 09 (01) ◽  
pp. 1-45 ◽  
Author(s):  
JØRGEN ELLEGAARD ANDERSEN
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Teichmüller Space ◽  
Closed Surface ◽  
Teichmuller Space ◽  
Open Dense Subset ◽  
Complex Structures ◽  
Thurston Boundary ◽  
Simply Connected ◽  
Singular Metric

Given a foliation F with closed leaves and with certain kinds of singularities on an oriented closed surface Σ, we construct in this paper an isotropic foliation on ℳ(Σ), the moduli space of flat G-connections, for G any compact simple simply connected Lie-group. We describe the infinitesimal structure of this isotropic foliation in terms of the basic cohomology with twisted coefficients of F. For any pair (F, g), where g is a singular metric on Σ compatible with F, we construct a new polarization on the symplectic manifold ℳ′(Σ), the open dense subset of smooth points of ℳ(Σ). We construct a sequence of complex structures on Σ, such that the corresponding complex structures on ℳ′(Σ) converges to the polarization associated to (F, g). In particular we see that the Jeffrey–Weitzman polarization on the SU(2)-moduli space is the limit of a sequence of complex structures induced from a degenerating family of complex structures on Σ, which converges to a point in the Thurston boundary of Teichmüller space of Σ. As a corollary of the above constructions, we establish a certain discontinuiuty at the Thurston boundary of Teichmüller space for the map from Teichmüller space to the space of polarizations on ℳ′(Σ). For any reducible finite order diffeomorphism of the surface, our constuction produces an invariant polarization on the moduli space.

THE ADLER-BARDEEN THEOREM FOR THE AXIAL U(1) ANOMALY IN A GENERAL NON-ABELIAN GAUGE THEORY

1987 ◽  
Vol 02 (02) ◽  
pp. 385-407 ◽  
Author(s):  
CLAUDIO LUCCHESI ◽  
OLIVIER PIGUET ◽  
KLAUS SIBOLD
Keyword(s):  
Gauge Theory ◽  
Gauge Group ◽  
Axial Current ◽  
Compact Lie Group ◽  
Zero Energy ◽  
Abelian Gauge ◽  
Regularization Scheme ◽  
Abelian Gauge Theory ◽  
Abelian Case ◽  
Finiteness Properties

A general, regularization-scheme-independent proof of the nonrenormalization theorem for the anomaly of a U(1) axial current in a renormalizable gauge theory is presented. The gauge group may be an arbitrary compact Lie group. The validity of the theorem is traced back to some finiteness properties allowing for a well defined but particular choice of the anomaly operators. Whereas in the case of a purely Abelian gauge group this choice amounts to a physically reasonable normalization at zero energy, the general non-Abelian case awaits a deeper understanding.

scholarly journals On Moduli Spaces of Positive Scalar Curvature Metrics on Highly Connected Manifolds

2020 ◽  
Author(s):  
Michael Wiemeler
Keyword(s):  
Fundamental Group ◽  
Scalar Curvature ◽  
Moduli Space ◽  
Moduli Spaces ◽  
Positive Scalar Curvature ◽  
Spin Manifold ◽  
Homotopy Groups ◽  
Positive Scalar ◽  
Simply Connected ◽  
Highly Connected Manifolds

Abstract Let $M$ be a simply connected spin manifold of dimension at least six, which admits a metric of positive scalar curvature. We show that the observer moduli space of positive scalar curvature metrics on $M$ has non-trivial higher homotopy groups. Moreover, denote by $\mathcal{M}_0^+(M)$ the moduli space of positive scalar curvature metrics on $M$ associated to the group of orientation-preserving diffeomorphisms of $M$. We show that if $M$ belongs to a certain class of manifolds that includes $(2n-2)$-connected $(4n-2)$-dimensional manifolds, then the fundamental group of $\mathcal{M}_0^+(M)$ is non-trivial.

scholarly journals STANDARD MODEL BUNDLES OF THE HETEROTIC STRING

2006 ◽  
Vol 21 (06) ◽  
pp. 1261-1281 ◽  
Author(s):  
GOTTFRIED CURIO
Keyword(s):  
Standard Model ◽  
Spectral Data ◽  
Gauge Group ◽  
Matter Content ◽  
Heterotic String ◽  
Spectral Cover ◽  
The Standard Model ◽  
Free Involution ◽  
Simply Connected ◽  
Calabi Yau Manifolds

We show how to construct supersymmetric three-generation models with gauge group and matter content of the Standard Model in the framework of non-simply-connected elliptically fibered Calabi–Yau manifolds Z. The elliptic fibration on a cover Calabi–Yau, where the model has six generations of SU(5) and the bundle is given via the spectral cover description, has a second section leading to the needed free involution. The relevant involution on the defining spectral data of the bundle is identified for a general Calabi–Yau of this type and invariant bundles are generally constructible.

FOUR-DIMENSIONAL HETEROTIC STRING MODELS WITH SU(3) × SU(2) × Up(1) LOW ENERGY GAUGE GROUP

1989 ◽  
Vol 04 (17) ◽  
pp. 4475-4485 ◽  
Author(s):  
DAVID BAILIN ◽  
ALEX LOVE
Keyword(s):  
Gauge Group ◽  
Degrees Of Freedom ◽  
Low Energy ◽  
Heterotic String ◽  
String Models

A study is made of a class of four-dimensional heterotic string models with complex fermionic degrees of freedom to discover whether there are any examples with 3 or 4 generations of quarks and leptons and SU C(3) × SU L(2) × U p(1) low energy gauge group.

FIXED POINT FREE CIRCLE ACTIONS AND FINITENESS THEOREMS

2000 ◽  
Vol 02 (01) ◽  
pp. 75-86 ◽  
Author(s):  
FUQUAN FANG ◽  
XIAOCHUN RONG
Keyword(s):  
Fixed Point ◽  
Fundamental Group ◽  
Fundamental Groups ◽  
Vanishing Theorem ◽  
Fixed Point Set ◽  
Circle Actions ◽  
Finite Fundamental Group ◽  
Finiteness Theorems ◽  
Point Set ◽  
Simply Connected

We prove a vanishing theorem of certain cohomology classes for an 2n-manifold of finite fundamental group which admits a fixed point free circle action. In particular, it implies that any Tk-action on a compact symplectic manifold of finite fundamental group has a non-empty fixed point set. The vanishing theorem is used to prove two finiteness results in which no lower bound on volume is assumed. (i) The set of symplectic n-manifolds of finite fundamental groups with curvature, λ ≤ sec ≤ Λ, and diameter, diam ; ≤ d, contains only finitely many diffeomorphism types depending only on n, λ, Λ and d. (ii) The set of simply connected n-manifolds (n ≤ 6) with λ ≤ sec ≤ Λ and diam ≤ d contains only finitely many diffeomorphism types depending only on n, λ, Λ and d.

scholarly journals On the Connectedness of Moduli Spaces of Flat Connections over Compact Surfaces

2004 ◽  
Vol 56 (6) ◽  
pp. 1228-1236 ◽  
Author(s):  
Nan-Kuo Ho ◽  
Chiu-Chu Melissa Liu
Keyword(s):  
Lie Groups ◽  
Moduli Space ◽  
Moduli Spaces ◽  
Orientable Surface ◽  
Equivalence Classes ◽  
Nonorientable Surface ◽  
Flat Connections ◽  
Gauge Equivalence ◽  
Compact Orientable Surface ◽  
Simply Connected

AbstractWe study the connectedness of the moduli space of gauge equivalence classes of flat G-connections on a compact orientable surface or a compact nonorientable surface for a class of compact connected Lie groups. This class includes all the compact, connected, simply connected Lie groups, and some non-semisimple classical groups.

scholarly journals Exploring the landscape of heterotic strings on Td

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Anamaría Font ◽  
Bernardo Fraiman ◽  
Mariana Graña ◽  
Carmen A. Núñez ◽  
Héctor Parra De Freitas
Keyword(s):  
Gauge Group ◽  
Moduli Space ◽  
Relevant Information ◽  
Duality Group ◽  
Simple Method ◽  
Gauge Groups ◽  
Heterotic Strings ◽  
Singular Fibers ◽  
Special Points ◽  
Extended Dynkin Diagram

Abstract Compactifications of the heterotic string on Td are the simplest, yet rich enough playgrounds to uncover swampland ideas: the U(1)d+16 left-moving gauge symmetry gets enhanced at special points in moduli space only to certain groups. We state criteria, based on lattice embedding techniques, to establish whether a gauge group is realized or not. For generic d, we further show how to obtain the moduli that lead to a given gauge group by modifying the method of deleting nodes in the extended Dynkin diagram of the Narain lattice II1,17. More general algorithms to explore the moduli space are also developed. For d = 1 and 2 we list all the maximally enhanced gauge groups, moduli, and other relevant information about the embedding in IId,d+16. In agreement with the duality between heterotic on T2 and F-theory on K3, all possible gauge groups on T2 match all possible ADE types of singular fibers of elliptic K3 surfaces. We also present a simple method to transform the moduli under the duality group, and we build the map that relates the charge lattices and moduli of the compactification of the E8 × E8 and Spin(32)/ℤ2 heterotic theories.

NON-ABELIAN GAUGE THEORY FOR CHERN–SIMONS PATH INTEGRAL ON R3

2012 ◽  
Vol 21 (04) ◽  
pp. 1250039 ◽  
Author(s):  
ADRIAN P. C. LIM
Keyword(s):  
Gauge Theory ◽  
Gauge Group ◽  
Path Integral ◽  
Wilson Loop ◽  
Wiener Measure ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Chern Simons

In a prequel to this article, we used abstract Wiener measure to define the Chern–Simons path integral over ℝ3. In this sequel, we compute the Wilson Loop observable for the non-abelian gauge group and compare with current knot literature.

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