Mode Interactions of the Tachyon Condensate in p-adic String Theory

TL;DR

This paper analyzes fluctuations around tachyon-induced lumps in $p$-adic open string theory and discovers a discrete tower of fluctuation modes with mass-squared levels $m^2 = 2(n-1)$, starting from a tachyon ($n=0$) and including a massless mode at $n=1$. Using a nonlocal tachyon action and Hermite-basis expansion, it derives the interaction structure among fluctuations, characterised by combinatorial coefficients $A_{n_1\ldots n_\ell}$ that count contractions. It then shows that the $N$-point amplitudes for excited, transverse-to-brane states reproduce the $p$-adic tachyon amplitudes up to the same combinatorial factor $A_{n_1\ldots n_N}$, with poles factorizing according to internal states of mass $m_I^2 = 2(n_I-1)$. Collectively, these results support a consistent open-string interpretation of lump fluctuations within $p$-adic string theory and illuminate the role (and apparent absence) of gauge fields in this framework, with implications for lump descent and possible closed-string generalizations.

Abstract

We study the fluctuation modes for lump solutions of the tachyon effective potential in p-adic open string theory. We find a discrete spectrum with equally spaced mass squared levels. We also find that the interactions derived from this field theory are consistent with p-adic string amplitudes for excited string states.

Figures (1)

• Figure 1: Factorization of the amplitude with incoming momenta $k_i$ and mode number $n_i$ about a pole with momentum $k_I$ and mode number $n_I$.