[Paper Review] Cosmic Strings with Small Tension

Edi Halyo|ArXiv.org|Jun 15, 2009

Black Holes and Theoretical Physics44 references3 citations

TL;DR

This paper proposes that cosmic F-term strings with exponentially small tension arise from D3 branes wrapped on nodes of a deformed $A_3$ singularity, where brane instanton effects after a geometric transition induce an exponentially small effective volume, leading to tiny string tension. The model generalizes to non-Abelian cosmic strings stable against monopole-antimonopole pair creation.

ABSTRACT

We describe cosmic F--term strings with exponentially small tension which are D3 branes wrapped on deformed $A_3$ singularities. We show that brane instanton effects which can be calculated after a geometric transition give rise to an exponentially small volume for the node on which the D3 branes wrap leading to a string with small tension. We generalize our description to the case of non--Abelian cosmic strings and argue that these strings are stable against monopole--anti monopole pair creation.

Motivation & Objective

• To explain the origin of cosmic strings with extremely small tension in string theory, addressing the challenge of realizing such small tensions naturally.
• To show that brane instanton effects on a deformed $A_3$ singularity lead to an exponentially small effective volume for the D3 brane wrapping cycle.
• To demonstrate that this mechanism yields a calculable, exponentially suppressed string tension via nonperturbative effects after geometric transition.
• To generalize the construction to non-Abelian cosmic strings and establish their stability against monopole-antimonopole pair creation.
• To provide a framework for small-tension cosmic strings that could be detectable by future gravitational wave observatories like LIGO and LISA.

Proposed method

• Model the $A_3$ singularity as a fibration over the complex plane with three distinct nodes, each supporting a D5 brane or a D3 brane wrapped on a 2-cycle.
• Use the worldvolume theory of D5 branes on the nodes to describe F-term strings, with the superpotential encoding deformations via $W = \int (z_i(x) - z_{i+1}(x)) dx$.
• Apply brane instanton effects on one node (e.g., node 1) that induce a nonperturbative F-term, calculable after a geometric transition to a small-resolution Calabi-Yau.
• Relate the resulting exponentially small F-term to an exponentially small effective volume $V_2 \sim e^{-\alpha \phi}$ for the D3 brane wrapping node 2.
• Use the relation $T \sim g_s^{-1} V_2$ to derive the string tension, showing it is exponentially suppressed due to the instanton-induced volume suppression.
• Generalize to non-Abelian strings by wrapping multiple D5 branes on the nodes, preserving the $U(1)$ gauge group on the central node for vortex formation.

Experimental results

Research questions

• RQ1 How can cosmic strings in string theory achieve exponentially small tensions without relying on warping?
• RQ2 What role do brane instantons and geometric transitions play in generating exponentially small volumes for D-brane wrapped cycles?
• RQ3 Can F-term cosmic strings in $N=1$ supersymmetric theories be stabilized against monopole-antimonopole pair creation?
• RQ4 How do non-Abelian cosmic strings constructed from multiple D5 branes on a deformed $A_3$ singularity differ from their Abelian counterparts in stability and dynamics?
• RQ5 What observational signatures distinguish D3-brane-wrapped cosmic strings from field-theory vortices, particularly in gravitational wave emission or intercommutation?

Key findings

• The string tension of D3 branes wrapped on a node of a deformed $A_3$ singularity is exponentially small due to brane instanton effects on a different node.
• After a geometric transition, the instanton-induced nonperturbative effect leads to an exponentially small effective volume $V_2 \sim e^{-\alpha \phi}$ for the D3 brane wrapping cycle.
• The resulting string tension scales as $T \sim g_s^{-1} e^{-\alpha \phi}$, with $\alpha \phi$ large, yielding $GT_s \sim 10^{-10}$ to $10^{-12}$, within reach of LIGO and LISA.
• The model generalizes to non-Abelian cosmic strings by wrapping multiple D5 branes on the nodes, preserving the $U(1)$ gauge group on the central node.
• The cosmic strings are stable against monopole-antimonopole pair creation because the probability $P \approx 0$ due to the small F-term and $O(1)$ gauge coupling.
• The string worldsheet theory is expected to deviate from a standard gauge theory at high energies, described by a Born–Infeld action, suggesting potential high-energy observational differences from field-theory vortices.