scholarly journals Symmetry enhancements in 7d heterotic strings

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Bernardo Fraiman ◽  
Héctor Parra De Freitas
Keyword(s):  
Gauge Group ◽  
Moduli Space ◽  
Space Exploration ◽  
Heterotic String ◽  
Complete List ◽  
Rank Reduction ◽  
Gauge Groups ◽  
Heterotic Strings ◽  
M Theory ◽  
Global Data

Abstract We use a moduli space exploration algorithm to produce a complete list of maximally enhanced gauge groups that are realized in the heterotic string in 7d, encompassing the usual Narain component, and five other components with rank reduction realized via nontrivial holonomy triples. Using lattice embedding techniques we find an explicit match with the mechanism of singularity freezing in M-theory on K3. The complete global data for each gauge group is explicitly given.

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.

scholarly journals Non-perturbative heterotic duals of M-theory on G2 orbifolds

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Bobby Samir Acharya ◽  
Alex Kinsella ◽  
David R. Morrison
Keyword(s):  
Heterotic String ◽  
Type I ◽  
Gauge Groups ◽  
M Theory ◽  
Degeneration Limit

Abstract By fibering the duality between the E8 × E8 heterotic string on T3 and M-theory on K3, we study heterotic duals of M-theory compactified on G2 orbifolds of the form T7/$$ {\mathbb{Z}}_2^3 $$ ℤ 2 3 . While the heterotic compactification space is straightforward, the description of the gauge bundle is subtle, involving the physics of point-like instantons on orbifold singularities. By comparing the gauge groups of the dual theories, we deduce behavior of a “half-G2” limit, which is the M-theory analog of the stable degeneration limit of F-theory. The heterotic backgrounds exhibit point-like instantons that are localized on pairs of orbifold loci, similar to the “gauge-locking” phenomenon seen in Hořava-Witten compactifications. In this way, the geometry of the G2 orbifold is translated to bundle data in the heterotic background. While the instanton configuration looks surprising from the perspective of the E8 × E8 heterotic string, it may be understood as T-dual Spin(32)/ℤ2 instantons along with winding shifts originating in a dual Type I compactification.

THE SUPERBRANCH POINTS AND TWO-LOOP CORRECTION IN THE HETEROTIC STRING THEORY

1988 ◽  
Vol 03 (01) ◽  
pp. 91-108 ◽  
Author(s):  
M. Bershadsky
Keyword(s):  
String Theory ◽  
Moduli Space ◽  
Heterotic String ◽  
Total Derivative ◽  
Loop Correction ◽  
Heterotic String Theory ◽  
Gauge Groups ◽  
Spin Structures ◽  
Conformal Field ◽  
Heterotic String Theories

In this paper we discuss the notion of superbranch point. The conformal field simulating the superbranch point is constructed. Using this field we construct the two-loop correction in the heterotic string theories (for the theories with gauge groups SO (32) and E8×E8). The contribution from different spin structures cancel each other but only up to the total derivative over the moduli space.

HOMOTOPY DECOMPOSITIONS OF GAUGE GROUPS OVER RIEMANN SURFACES AND APPLICATIONS TO MODULI SPACES

2011 ◽  
Vol 22 (12) ◽  
pp. 1711-1719 ◽  
Author(s):  
STEPHEN D. THERIAULT
Keyword(s):  
Riemann Surface ◽  
Gauge Group ◽  
Moduli Space ◽  
Moduli Spaces ◽  
Riemann Surfaces ◽  
Vector Bundles ◽  
Homotopy Groups ◽  
Gauge Groups ◽  
Stable Vector Bundles

For a prime p, the gauge group of a principal U(p)-bundle over a compact, orientable Riemann surface is decomposed up to homotopy as a product of spaces, each of which is commonly known. This is used to deduce explicit computations of the homotopy groups of the moduli space of stable vector bundles through a range, answering a question of Daskalopoulos and Uhlenbeck.

scholarly journals Explicit soft supersymmetry breaking in the heterotic M-theory B − L MSSM

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Anthony Ashmore ◽  
Sebastian Dumitru ◽  
Burt A. Ovrut
Keyword(s):  
Line Bundle ◽  
Supersymmetry Breaking ◽  
Moduli Space ◽  
Initial Conditions ◽  
Low Energy ◽  
Strongly Coupled ◽  
Hidden Sector ◽  
Effective Lagrangian ◽  
Soft Supersymmetry Breaking ◽  
M Theory

Abstract The strongly coupled heterotic M-theory vacuum for both the observable and hidden sectors of the B − L MSSM theory is reviewed, including a discussion of the “bundle” constraints that both the observable sector SU(4) vector bundle and the hidden sector bundle induced from a single line bundle must satisfy. Gaugino condensation is then introduced within this context, and the hidden sector bundles that exhibit gaugino condensation are presented. The condensation scale is computed, singling out one line bundle whose associated condensation scale is low enough to be compatible with the energy scales available at the LHC. The corresponding region of Kähler moduli space where all bundle constraints are satisfied is presented. The generic form of the moduli dependent F-terms due to a gaugino superpotential — which spontaneously break N = 1 supersymmetry in this sector — is presented and then given explicitly for the unique line bundle associated with the low condensation scale. The moduli-dependent coefficients for each of the gaugino and scalar field soft supersymmetry breaking terms are computed leading to a low-energy effective Lagrangian for the observable sector matter fields. We then show that at a large number of points in Kähler moduli space that satisfy all “bundle” constraints, these coefficients are initial conditions for the renormalization group equations which, at low energy, lead to completely realistic physics satisfying all phenomenological constraints. Finally, we show that a substantial number of these initial points also satisfy a final constraint arising from the quadratic Higgs-Higgs conjugate soft supersymmetry breaking term.

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.

scholarly journals EXTREMAL CASES OF RAPOPORT–ZINK SPACES

2021 ◽  
pp. 1-56
Author(s):  
Ulrich Görtz ◽  
Xuhua He ◽  
Michael Rapoport
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Complete List ◽  
Qualitative Properties ◽  
Model Case ◽  
Divisible Groups

Abstract We investigate qualitative properties of the underlying scheme of Rapoport–Zink formal moduli spaces of p-divisible groups (resp., shtukas). We single out those cases where the dimension of this underlying scheme is zero (resp., those where the dimension is the maximal possible). The model case for the first alternative is the Lubin–Tate moduli space, and the model case for the second alternative is the Drinfeld moduli space. We exhibit a complete list in both cases.

scholarly journals On TCS G2 manifolds and 4D emergent strings

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Fengjun Xu
Keyword(s):  
Moduli Space ◽  
Quantum Corrections ◽  
Type Ii ◽  
Quantum Level ◽  
Weakly Coupled ◽  
G2 Manifolds ◽  
Fundamental Type ◽  
M Theory ◽  
Distance Limit ◽  
Refined Version

Abstract In this note, we study the Swampland Distance Conjecture in TCS G2 manifold compactifications of M-theory. In particular, we are interested in testing a refined version — the Emergent String Conjecture, in settings with 4d N = 1 supersymmetry. We find that a weakly coupled, tensionless fundamental heterotic string does emerge at the infinite distance limit characterized by shrinking the K3-fiber in a TCS G2 manifold. Such a fundamental tensionless string leads to the parametrically leading infinite tower of asymptotically massless states, which is in line with the Emergent String Conjecture. The tensionless string, however, receives quantum corrections. We check that these quantum corrections do modify the volume of the shrinking K3-fiber via string duality and hence make the string regain a non-vanishing tension at the quantum level, leading to a decompactification. Geometrically, the quantum corrections modify the metric of the classical moduli space and are expected to obstruct the infinite distance limit. We also comment on another possible type of infinite distance limit in TCS G2 compactifications, which might lead to a weakly coupled fundamental type II string theory.

ENERGY REPRESENTATIONS OF INFINITE DIMENSIONAL GAUGE GROUPS IN NONCOMMUTATIVE GEOMETRY

1994 ◽  
Vol 05 (03) ◽  
pp. 329-348
Author(s):  
JEAN MARION
Keyword(s):  
Gauge Group ◽  
Noncommutative Geometry ◽  
Von Neumann Algebra ◽  
Linear Operators ◽  
Consistent Theory ◽  
Bounded Linear ◽  
Von Neumann ◽  
Gauge Groups ◽  
Infinite Dimensional ◽  
Involutive Algebra

Let M be a compact smooth manifold, let [Formula: see text] be a unital involutive subalgebra of the von Neumann algebra £ (H) of bounded linear operators of some Hilbert space H, let [Formula: see text] be the unital involutive algebra [Formula: see text], let [Formula: see text] be an hermitian projective right [Formula: see text]-module of finite type, and let [Formula: see text] be the gauge group of unitary elements of the unital involutive algebra [Formula: see text] of right [Formula: see text]-linear endomorphisms of [Formula: see text]. We first prove that noncommutative geometry provides the suitable setting upon which a consistent theory of energy representations [Formula: see text] can be built. Three series of energy representations are constructed. The first consists of energy representations of the gauge group [Formula: see text], [Formula: see text] being the group of unitary elements of [Formula: see text], associated with integrable Riemannian structures of M, and the second series consists of energy representations associated with (d, ∞)-summable K-cycles over [Formula: see text]. In the case where [Formula: see text] is a von Neumann algebra of type II 1 a third series is given: we introduce the notion of regular quasi K-cycle, we prove that regular quasi K-cycles over [Formula: see text] always exist, and that each of them induces an energy representation.

scholarly journals GENERAL BPS BLACK HOLES IN FIVE DIMENSIONS

1998 ◽  
Vol 13 (03) ◽  
pp. 239-252 ◽  
Author(s):  
W. A. SABRA
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Phase Transitions ◽  
Moduli Space ◽  
Arbitrary Number ◽  
Five Dimensions ◽  
Geometry Structure ◽  
Static Black Hole ◽  
Hole Configuration ◽  
M Theory

An algorithm for constructing general static black hole configuration for the theory of N=2, d= 5 supergravity coupled to an arbitrary number of Abelain vector multiplets is given. The underlying very special geometry structure plays a major role in this construction. From the viewpoint of M-theory compactified on a Calabi–Yau threefold, these black holes are identified with BPS winding states of the membrane around two-cycles of the Calabi–Yau threefold, and thus are of importance in the probing of the phase transitions in the moduli space of M-theory compactified on a Calabi–Yau threefold.

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