scholarly journals The prequantum line bundle on the moduli space of flat SU(N) connections on a Riemann surface and the homotopy of the large N limit

2017 ◽  
Vol 107 (9) ◽  
pp. 1581-1589 ◽  
Author(s):  
Lisa C. Jeffrey ◽  
Daniel A. Ramras ◽  
Jonathan Weitsman
Keyword(s):  
Riemann Surface ◽  
Line Bundle ◽  
Moduli Space ◽  
Large N

scholarly journals The dimension of the Hilbert space of geometric quantization of vortices on a Riemann surface

2017 ◽  
Vol 14 (10) ◽  
pp. 1750144
Author(s):  
Rukmini Dey ◽  
Saibal Ganguli
Keyword(s):  
Hilbert Space ◽  
Riemann Surface ◽  
Line Bundle ◽  
Euler Characteristic ◽  
Moduli Space ◽  
Geometric Quantization

In this paper, we calculate the dimension of the Hilbert space of Kähler quantization of the moduli space of vortices on a Riemann surface. This dimension is given by the holomorphic Euler characteristic of the quantum line bundle.

scholarly journals CHEN–RUAN COHOMOLOGY OF SOME MODULI SPACES, II

2010 ◽  
Vol 21 (04) ◽  
pp. 497-522 ◽  
Author(s):  
INDRANIL BISWAS ◽  
MAINAK PODDAR
Keyword(s):  
Riemann Surface ◽  
Line Bundle ◽  
Prime Number ◽  
Moduli Space ◽  
Moduli Spaces ◽  
Vector Bundles ◽  
Line Bundles ◽  
Holomorphic Line Bundle ◽  
Stable Vector Bundles

Let X be a compact connected Riemann surface of genus at least two. Let r be a prime number and ξ → X a holomorphic line bundle such that r is not a divisor of degree ξ. Let [Formula: see text] denote the moduli space of stable vector bundles over X of rank r and determinant ξ. By Γ we will denote the group of line bundles L over X such that L⊗r is trivial. This group Γ acts on [Formula: see text] by the rule (E, L) ↦ E ⊗ L. We compute the Chen–Ruan cohomology of the corresponding orbifold.

scholarly journals On moduli spaces of Hitchin pairs

2011 ◽  
Vol 151 (3) ◽  
pp. 441-457 ◽  
Author(s):  
INDRANIL BISWAS ◽  
PETER B. GOTHEN ◽  
MARINA LOGARES
Keyword(s):  
Riemann Surface ◽  
Line Bundle ◽  
Moduli Space ◽  
Moduli Spaces ◽  
Isomorphism Class ◽  
Compact Riemann Surface ◽  
List Type ◽  
Holomorphic Line Bundle ◽  
Type Number ◽  
Additional Hypothesis

AbstractLetXbe a compact Riemann surfaceXof genus at–least two. Fix a holomorphic line bundleLoverX. Letbe the moduli space of Hitchin pairs (E, φ ∈H0(End0(E) ⊗L)) overXof rankrand fixed determinant of degreed. The following conditions are imposed:(i)deg(L) ≥ 2g−2,r≥ 2, andL⊗rKX⊗r;(ii)(r, d) = 1; and(iii)ifg= 2 thenr≥ 6, and ifg= 3 thenr≥ 4.We prove that that the isomorphism class of the varietyuniquely determines the isomorphism class of the Riemann surfaceX. Moreover, our analysis shows thatis irreducible (this result holds without the additional hypothesis on the rank for low genus).

scholarly journals THE VERLINDE FORMULA FOR PARABOLIC BUNDLES

2001 ◽  
Vol 63 (3) ◽  
pp. 754-768 ◽  
Author(s):  
LISA C. JEFFREY
Keyword(s):  
Riemann Surface ◽  
Line Bundle ◽  
Conjugacy Class ◽  
Fundamental Group ◽  
Moduli Space ◽  
Boundary Component ◽  
Compact Riemann Surface ◽  
Central Element ◽  
Parabolic Bundles ◽  
Verlinde Formula

Let Σg be a compact Riemann surface of genus g, and G = SU(n). The central element c = diag(e2πid/n, …, e2πid/n) for d coprime to n is introduced. The Verlinde formula is proved for the Riemann–Roch number of a line bundle over the moduli space [Mscr ]g, 1(c, Λ) of representations of the fundamental group of a Riemann surface of genus g with one boundary component, for which the loop around the boundary is constrained to lie in the conjugacy class of cexp(Λ) (for Λ ∈ t+), and also for the moduli space [Mscr ]g, b(c, Λ) of representations of the fundamental group of a Riemann surface of genus g with s + 1 boundary components for which the loop around the 0th boundary component is sent to the central element c and the loop around the jth boundary component is constrained to lie in the conjugacy class of exp(Λ(j)) for Λ(j) ∈ t+. The proof is valid for Λ(j) in suitable neighbourhoods of 0.

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 A pathological case of the C1 conjecture in mixed characteristic

2018 ◽  
Vol 167 (01) ◽  
pp. 61-64 ◽  
Author(s):  
INDER KAUR
Keyword(s):  
Line Bundle ◽  
Moduli Space ◽  
Projective Curve ◽  
Free Sheaf ◽  
Smooth Projective Curve ◽  
Mixed Characteristic ◽  
Locally Free Sheaf ◽  
Fixed Rank ◽  
Pathological Case

AbstractLet K be a field of characteristic 0. Fix integers r, d coprime with r ⩾ 2. Let XK be a smooth, projective, geometrically connected curve of genus g ⩾ 2 defined over K. Assume there exists a line bundle ${\cal L}_K$ on XK of degree d. In this paper we prove the existence of a stable locally free sheaf on XK with rank r and determinant ${\cal L}_K$. This trivially proves the C1 conjecture in mixed characteristic for the moduli space of stable locally free sheaves of fixed rank and determinant over a smooth, projective curve.

Equivariant Forms: Structure and Geometry

2013 ◽  
Vol 56 (3) ◽  
pp. 520-533 ◽  
Author(s):  
Abdelkrim Elbasraoui ◽  
Abdellah Sebbar
Keyword(s):  
Riemann Surface ◽  
Line Bundle ◽  
Modular Forms ◽  
Differential Forms ◽  
Cross Ratio ◽  
Canonical Line Bundle ◽  
The Cross

Abstract.In this paper we study the notion of equivariant forms introduced in the authors' previous works. In particular, we completely classify all the equivariant forms for a subgroup of SL2(ℤ) by means of the cross-ratio, weight 2 modular forms, quasimodular forms, as well as differential forms of a Riemann surface and sections of a canonical line bundle.

scholarly journals Normal functions and the height of Gross-Schoen cycles

2014 ◽  
Vol 214 ◽  
pp. 53-77 ◽  
Author(s):  
Robin De Jong
Keyword(s):  
Line Bundle ◽  
Moduli Space ◽  
The Self ◽  
Compact Type ◽  
Stable Curves ◽  
Normal Functions ◽  
Chern Form ◽  
Bloch Line ◽  
Pointed Curve ◽  
Dualizing Sheaf

AbstractWe prove a variant of a formula due to Zhang relating the Beilinson– Bloch height of the Gross–Schoen cycle on a pointed curve with the self-intersection of its relative dualizing sheaf. In our approach, the height of the Gross–Schoen cycle occurs as the degree of a suitable Bloch line bundle. We show that the Chern form of this line bundle is nonnegative, and we calculate its class in the Picard group of the moduli space of pointed stable curves of compact type. The basic tools are normal functions and biextensions associated to the cohomology of the universal Jacobian.

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