Large Marginal Deformations in String Field Theory

TL;DR

This paper investigates large marginal deformations in open bosonic string field theory by applying level truncation to compute the effective potential for the marginal field associated with a Wilson line. By solving all other fields as functions of the massless mode $a_s$, the authors show the effective potential flattens as the level increases, but the deformation parameter is defined only within a finite range $|a_s|\le \overline a_s$ due to a merger of two solution branches. They demonstrate a precise mapping between Wilson-line marginals and tachyon-lump marginals at the critical radius $R=1$, including an isomorphism $t_1 = \sqrt{2}\, a_s$ up to level $(4,8)$ and discuss how the CFT marginal parameter $a_c$ may relate to the string-field parameter through various scenarios. The work highlights how open string field theory encodes the full CFT moduli space via branch structure and coordinate patches, and it connects marginal deformations to both Wilson lines and lump solutions on a circle, with implications for understanding moduli spaces in string theory.

Abstract

We use the level truncation scheme to obtain accurate descriptions of open bosonic string field configurations corresponding to large marginal deformations such as background Wilson lines. To do so, we solve for all fields as functions of the massless string field, and confirm that the effective potential of the massless field becomes increasingly flat as the level of approximation is increased. Surprisingly, as a result of the merging of two branches of the solution - one originating at zero tachyon vev and the other originating at the tachyonic vacuum - this effective potential exists only for a finite range of values of the massless field. We use the D1 to D0 brane marginal transition on a circle to explore the possibility that this finite range corresponds to the infinite range of the conformal field theory parameter describing marginal deformations, but are unable to arrive at a definitive conclusion.

Figures (4)

• Figure 1: The level (1,2) effective potential $V\equiv (2\pi^2 {\cal V}^{M/V}(a_s))$ for $a_s$ on the $M$-branch (solid line) and $V$-branch (dashed line). The two branches meet at $a_s^{(1,2)} = 8/27$.
• Figure 2: The various effective potentials $V\equiv(2\pi^2 {\cal V}^{M}(a_s))$ for the marginal parameter $a_s$ on the $M$-branch. The dashed curve represents the level (1,2) approximation, the successively flatter curves represent the level (2,4), (3,6) and (4,8) approximations. Note that each potential has a different domain of definition.
• Figure 3: The various effective potentials $V\equiv(2\pi^2 {\cal V}^{V}(a_s))$ for the marginal parameter $a_s$ on the $V$-branch. The top curve represents the level (1,2) approximation, the successively lower curves represent the level (2,4), (3,6) and (4,8) approximations.
• Figure 4: The level (1,2), (2,4), (3, 6) and (4,8) effective potentials $V\equiv 2\pi^2\widetilde{\cal V}^M (t_1;R)$ for $t_1$ when $R= \sqrt{1.1}$. As the level is increased the potentials become deeper and the value of $t_1$ at the minimum larger.