Codimension two lump solutions in string field theory and tachyonic theories

TL;DR

The paper addresses codimension-two lump solitons in open bosonic string field theory and two tachyonic models, using level truncation on a two-torus to probe their structure. It computes the potential including momentum modes and builds lumps at level $(2,4)$ with $R=\sqrt{3}$, reporting a tension ratio of $r^{(2)}_{(2,4)}\approx 1.13025$ and radius-independent profiles when compared to $R=3$. Lumps exist in pure tachyonic SFT and in pure $\phi^3$ theory, with faster convergence in the tachyonic model thanks to the $K^{3-\text{level}}$ factors. Overall, the work supports using tachyonic toy models to study SFT solitons and highlights how level truncation can capture key qualitative features despite different convergence properties.

Abstract

We present some solutions for lumps in two dimensions in level-expanded string field theory, as well as in two tachyonic theories: pure tachyonic string field theory and pure $φ^3$ theory. Much easier to handle, these theories might be used to help understanding solitonic features of string field theory. We compare lump solutions between these theories and we discuss some convergence issues.

Figures (6)

• Figure 1: A lump in sft at level (2, 4) with $R=\sqrt{3}$. The plot represents $-t(x, y)$ as a function of $x$ and $y$.
• Figure 2: A lump in sft at level (2, 4) with $R=3$. The plot represents $-t(x, y)$ as a function of $x$ and $y$.
• Figure 3: The dashed curve is the profile $-t(x,0)$ of the lump solution in sft at $R=\sqrt{3}$, the solid curve is the profile $-t(x,0)$ of the lump solution at $R=3$
• Figure 4: Lump profiles $-t(x,0)$ in string field theory (solid curve), pure tachyonic sft (dashed curve) and pure $\phi^3$ theory (dotted curve) at level (2, 4) and $R=3$.
• Figure 5: Lump profiles $-t(x,0)$ in pure tachyonic sft with $R=3$, at level (2, 4) (dashed curve), (3, 9) (dotted curve) and (10, 30) (solid curve)