scholarly journals Non-flat elliptic four-folds, three-form cohomology and strongly coupled theories in four dimensions

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Paul-Konstantin Oehlmann
Keyword(s):  
Riemann Surfaces ◽  
Coulomb Branch ◽  
Strongly Coupled ◽  
Four Dimensions ◽  
Isolated Points ◽  
Hodge Numbers ◽  
Higher Rank ◽  
Compact Riemann Surfaces ◽  
M Theory ◽  
String Theories

Abstract In this note we consider smooth elliptic Calabi-Yau four-folds whose fiber ceases to be flat over compact Riemann surfaces of genus g in the base. These non-flat fibers contribute Kähler moduli to the four-fold but also add to the three-form cohomology for g > 0. In F-/M-theory these sectors are to be interpreted as compactifications of six/five dimensional $$ \mathcal{N} $$ N = (1, 0) superconformal matter theories. The three-form cohomology leads to additional chiral singlets proportional to the dimension of five dimensional Coulomb branch of those sectors. We construct explicit examples for E-string theories as well as higher rank cases. For the E-string theories we further investigate conifold transitions that remove those non-flat fibers. First we show how non-flat fibers can be deformed from curves down to isolated points in the base. This removes the chiral singlet of the three-forms and leads to non-perturbative four-point couplings among matter fields which can be understood as remnants of the former E-string. Alternatively the non-flat fibers can be avoided by performing birational base changes analogous to 6D tensor branches. For compact bases these transitions alternate all Hodge numbers but leave the Euler number invariant.

scholarly journals Isospectral flat connexions

2013 ◽  
Vol 31 (2) ◽  
pp. 279
Author(s):  
S. Srinivas Rau ◽  
Sudhamsh Reddy
Keyword(s):  
Riemann Surfaces ◽  
Higher Rank ◽  
Compact Riemann Surfaces

Isospectral flat connexions are constructed for higher rank bundlesover compact Riemann surfaces

scholarly journals FOUR LECTURES ON THE GAUGE/GRAVITY CORRESPONDENCE

2003 ◽  
Vol 18 (31) ◽  
pp. 5647-5711 ◽  
Author(s):  
MATTEO BERTOLINI
Keyword(s):  
Gauge Theory ◽  
Riemann Surfaces ◽  
Gauge Theories ◽  
Open Problems ◽  
Four Dimensions ◽  
General Overview ◽  
Geometric Transitions ◽  
Supersymmetric Gauge ◽  
Gauge Gravity ◽  
M Theory

We review in a pedagogical manner some of the efforts aimed at extending the gauge/gravity correspondence to nonconformal supersymmetric gauge theories in four dimensions. After giving a general overview, we discuss in detail two specific examples: fractional D-branes on orbifolds and D-branes wrapped on supersymmetric cycles of Calabi–Yau spaces. We explore in particular which gauge theory information can be extracted from the corresponding supergravity solutions, and what the remaining open problems are. We also briefly explain the connection between these and other approaches, such as fractional branes on conifolds, branes suspended between branes, M5-branes on Riemann surfaces and M-theory on G2-holonomy manifolds, and discuss the role played by geometric transitions in all that.

scholarly journals On the existence of connected components of dimension one in the branch locus of moduli spaces of riemann surfaces

2012 ◽  
Vol 111 (1) ◽  
pp. 53 ◽  
Author(s):  
Antonio F. Costa ◽  
Milagros Izquierdo
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Riemann Surfaces ◽  
Fuchsian Groups ◽  
Connected Components ◽  
Branch Locus ◽  
Isolated Points ◽  
Compact Riemann Surfaces ◽  
Dimension One ◽  
Substantial Interest

Let $g$ be an integer $\geq3$ and let $B_{g}=\{X\in\mathcal{M}_{g}: \mathrm{Aut}(X)\neq Id\}$ be the branch locus of $M_{g}$, where $M_{g}$ denotes the moduli space of compact Riemann surfaces of genus $g$. The structure of $B_{g}$ is of substantial interest because $B_{g}$ corresponds to the singularities of the action of the modular group on the Teichmüller space of surfaces of genus $g$ (see [14]). Kulkarni ([15], see also [13]) proved the existence of isolated points in the branch loci of the moduli spaces of Riemann surfaces. In this work we study the isolated connected components of dimension 1 in such loci. These isolated components of dimension one appear if the genus is $g=p-1$ with $p$ prime $\geq11$. We use uniformization by Fuchsian groups and the equisymmetric stratification of the branch loci.

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.

A Hodge theoretic projective structure on compact Riemann surfaces

2021 ◽  
Vol 149 ◽  
pp. 1-27
Author(s):  
Indranil Biswas ◽  
Elisabetta Colombo ◽  
Paola Frediani ◽  
Gian Pietro Pirola
Keyword(s):  
Riemann Surfaces ◽  
Projective Structure ◽  
Compact Riemann Surfaces

scholarly journals Convergence of Discrete Period Matrices and Discrete Holomorphic Integrals for Ramified Coverings of the Riemann Sphere

2021 ◽  
Vol 24 (3) ◽  
Author(s):  
Alexander I. Bobenko ◽  
Ulrike Bücking
Keyword(s):  
Error Estimate ◽  
Branch Point ◽  
Riemann Surfaces ◽  
Riemann Sphere ◽  
Holomorphic Functions ◽  
Convergence Result ◽  
Edge Length ◽  
Ramified Covering ◽  
Compact Riemann Surfaces ◽  
Ramified Coverings

AbstractWe consider the class of compact Riemann surfaces which are ramified coverings of the Riemann sphere $\hat {\mathbb {C}}$ ℂ ̂ . Based on a triangulation of this covering we define discrete (multivalued) harmonic and holomorphic functions. We prove that the corresponding discrete period matrices converge to their continuous counterparts. In order to achieve an error estimate, which is linear in the maximal edge length of the triangles, we suitably adapt the triangulations in a neighborhood of every branch point. Finally, we also prove a convergence result for discrete holomorphic integrals for our adapted triangulations of the ramified covering.

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