Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Comments on the Emergence of 4D Topological Amplitudes in M-Theory

Manuel Artime, Ralph Blumenhagen, Aleksandar Gligovic, Panagiotis Leivadaros

Abstract

The M-theoretic Emergence Proposal claims that all of the terms in the low-energy action arise from quantum effects. After reviewing the current status of this proposal, we focus on four-dimensional compactifications with $N=2$ supersymmetry, where kinetic terms are encoded in topological string amplitudes, such as the prepotential $F_0$. Evidence for the emergence of such terms was provided recently, where in particular it was shown that the classical cubic term in $F_0$ can be obtained by integrating out the light towers of states in the M-theory limit, using a novel regularization of the infinite sum over Gopakumar/Vafa invariants. We address two issues that were left open. First, we show that the regularization can be equivalently performed in complex structure moduli space and in Kähler moduli space. Second, we extend the proposed regularization to the linear terms in the one-loop prepotential $F_1$.

Comments on the Emergence of 4D Topological Amplitudes in M-Theory

Abstract

The M-theoretic Emergence Proposal claims that all of the terms in the low-energy action arise from quantum effects. After reviewing the current status of this proposal, we focus on four-dimensional compactifications with supersymmetry, where kinetic terms are encoded in topological string amplitudes, such as the prepotential . Evidence for the emergence of such terms was provided recently, where in particular it was shown that the classical cubic term in can be obtained by integrating out the light towers of states in the M-theory limit, using a novel regularization of the infinite sum over Gopakumar/Vafa invariants. We address two issues that were left open. First, we show that the regularization can be equivalently performed in complex structure moduli space and in Kähler moduli space. Second, we extend the proposed regularization to the linear terms in the one-loop prepotential .
Paper Structure (11 sections, 49 equations, 3 figures, 1 table)

This paper contains 11 sections, 49 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Emergence of 4D N=2 topological couplings
  3. Preliminaries
  4. Regularization scheme for the prepotential F₀
  5. Limit in complex structure moduli space
  6. Limit in Kähler moduli space
  7. Regularization scheme for the 1-loop prepotential F₁
  8. Limit in complex structure moduli space
  9. Limit in Kähler moduli space
  10. Conclusion
  11. Acknowledgments.

Figures (3)

  • Figure 1: Trajectory $u\to0$ along the real axis and the branch-cut in the $u$-plane, given by the negative real axis, mapped to the $t$-plane using the mirror map \ref{['mirrormap']}.
  • Figure 2: Ratio of eq.\ref{['prepotint']} and eq.\ref{['prepotexp']} for $u\rightarrow0$.
  • Figure 3: Ratio of eq.\ref{['F1int']} and eq.\ref{['divexpF1']} for $u\rightarrow0$.