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String Memory Effect

Hamid Afshar, Erfan Esmaeili, M. M. Sheikh-Jabbari

TL;DR

This work investigates memory effects for NSNS 2-form (B-field) backgrounds probed by strings, defining a string memory effect for both closed and open strings and linking it to 2-form soft charges. In the closed-string sector, memory shows up as a rotation of internal oscillator modes controlled by the total change in the B-field, while the center-of-mass motion remains unaffected; in the open-string sector, memory appears as a changing noncommutativity parameter on D-branes and a time-dependent dipole moment, with oscillator modes largely invariant at leading order. The analysis combines worldsheet calculations, quantum S-matrix treatment, and an effective field theory perspective to connect memory to soft charges and the IR triangle, and employs boundary-state methods to explore D-brane probes. The results suggest a concrete framework for generalizing to higher-form memories and provide avenues to integrate these findings with superstring setups and compactifications, thereby enriching the understanding of IR structure in string theory. Overall, the paper clarifies how p-form memories manifest in string theory and offers a calculable approach to relate memory effects to asymptotic symmetries and soft theorems.

Abstract

In systems with local gauge symmetries, the memory effect corresponds to traces inscribed on a suitable probe when a pure gauge configuration at infinite past dynamically evolves to another pure gauge configuration at infinite future. In this work, we study the memory effect of 2-form gauge fields which is probed by strings. We discuss the "string memory effect" for closed and open strings at classical and quantum levels. The closed string memory is encoded in the internal excited modes of the string, and in the open string case, it is encoded in the relative position of the two endpoints and the noncommutativity parameter associated with the D-brane where the open string endpoints are attached. We also discuss 2-form memory with D-brane probes using boundary state formulation and, the relation between string memory and 2-form soft charges analyzed in [1].

String Memory Effect

TL;DR

This work investigates memory effects for NSNS 2-form (B-field) backgrounds probed by strings, defining a string memory effect for both closed and open strings and linking it to 2-form soft charges. In the closed-string sector, memory shows up as a rotation of internal oscillator modes controlled by the total change in the B-field, while the center-of-mass motion remains unaffected; in the open-string sector, memory appears as a changing noncommutativity parameter on D-branes and a time-dependent dipole moment, with oscillator modes largely invariant at leading order. The analysis combines worldsheet calculations, quantum S-matrix treatment, and an effective field theory perspective to connect memory to soft charges and the IR triangle, and employs boundary-state methods to explore D-brane probes. The results suggest a concrete framework for generalizing to higher-form memories and provide avenues to integrate these findings with superstring setups and compactifications, thereby enriching the understanding of IR structure in string theory. Overall, the paper clarifies how p-form memories manifest in string theory and offers a calculable approach to relate memory effects to asymptotic symmetries and soft theorems.

Abstract

In systems with local gauge symmetries, the memory effect corresponds to traces inscribed on a suitable probe when a pure gauge configuration at infinite past dynamically evolves to another pure gauge configuration at infinite future. In this work, we study the memory effect of 2-form gauge fields which is probed by strings. We discuss the "string memory effect" for closed and open strings at classical and quantum levels. The closed string memory is encoded in the internal excited modes of the string, and in the open string case, it is encoded in the relative position of the two endpoints and the noncommutativity parameter associated with the D-brane where the open string endpoints are attached. We also discuss 2-form memory with D-brane probes using boundary state formulation and, the relation between string memory and 2-form soft charges analyzed in [1].

Paper Structure

This paper contains 24 sections, 3 theorems, 108 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Organization of the paper.
  3. Worldsheet.
  4. Spacetime fields.
  5. Memory effect: review and remarks
  6. Classical treatment
  7. Electromagnetic Memory Effect.
  8. Quantum treatment
  9. Memory effect and conserved charges
  10. Two-form soft charges.
  11. Closed string memory effect
  12. Classical closed string memory effect.
  13. Quantum closed string memory
  14. Effective field theory analysis
  15. Gauge fixed action; TT gauge.
  16. ...and 9 more sections

Key Result

Proposition 1

Let a classical system $(p_n,q_n;H)$ interact through an external gauge potential $\mathcal{A}$ with time-dependent field strength $\mathcal{F}(u)$ which is vanishing at early and late times: so the system evolves with free Hamiltonian in the limit $u\to\pm\infty$.This is typically the case when $\mathcal{F}(u)$ is a radiative field which is strong only in a finite duration. Defining the pure gau

Figures (2)

  • Figure 1: Observation of memory effect due to the out-going radiation by massive probes. The $\odot_{1,2}$ symbols show detection points, located at constant $r$. One could set the detection times earlier to observe the in-going memory effect. The dashed lines depict some Cauchy surfaces and as we see they all intersect at spatial infinity $i_0$. In the figure we have implicitly imposed the antipodal matching through $i^0=\mathcal{I}^+_-=\mathcal{I}^-_+$.
  • Figure 2: Kinetic mixing vertices.

Theorems & Definitions (4)

  • Proposition 1
  • Definition 1: Memory effect
  • Proposition 2: Memory effect
  • Proposition 3