Symmetry Points of $\mathcal{N}=1$ Modular Geometry

Abstract

We consider 4d $\mathcal{N}=1$ supergravity theories with modular symmetry, where the modulus $\tau$ is the upper half-plane modulo $SL(2,\mathbf{Z})$ action. We focus on enhanced discrete gauge symmetry points $\tau =i,\exp (2\pi i/3)$, and argue that, if there are no new additional massless fields at these points, they will always be critical points of the scalar potential. Moreover, we show that whether these correspond to dS, AdS, or Minkowski vacua can be generically determined simply by the weight of the superpotential under modular transformations. We also analyze the asymptotics of the scalar potential and find that compatibility with the Swampland principles implies that, if nonvanishing, the scalar potential decays either exponentially or double-exponentially, and that the asymptotic slope is bounded. The slope is governed by the superpotential weight as well as by real-analytic modular contributions to the Kähler potential.

19 pages, references added; published version

References in corpus (22)

• Non-Perturbative Superpotentials In String Theory
• Supersymmetry Breaking and alpha'-Corrections to Flux Induced Potentials
• Effects of D-instantons
• What if string theory has no de Sitter vacua?
• Trans-Planckian Censorship and the Swampland
• Towards de Sitter from 10D
• The tension between 10D supergravity and dS uplifts
• Control issues of KKLT
• $H_0$ Tension, Swampland Conjectures and the Epoch of Fading Dark Matter
• A Non-Perturbative Superpotential With $E_8$ Symmetry
• Non-Perturbative Corrections and Modularity in N=1 Type IIB Compactifications
• Dimensional Reduction and (Anti) de Sitter Bounds
• Horizons cannot save the Landscape
• Modular Symmetries and the Swampland Conjectures
• Holography and the KKLT Scenario
• Persistent anti-brane singularities
• Heterotic de Sitter Beyond Modular Symmetry
• The LVS Parametric Tadpole Constraint
• A Class of N=1 Dual String Pairs and its Modular Superpotential
• LVS de Sitter Vacua are probably in the Swampland
• Superpotentials from Singular Divisors
• de Sitter Bubbles and the Swampland

Cited by in corpus (1)

• The CFT Distance Conjecture and Tensionless String Limits in $\mathcal{N}=2$ Quiver Gauge Theories