[Paper Review] Regge behavior saves String Theory from causality violations

G. D’Appollonio, P. Di Vecchia+2 more|arXiv (Cornell University)|Feb 4, 2015

Black Holes and Theoretical Physics14 references4 citations

TL;DR

This paper resolves causality violations in string theory caused by higher-derivative gravity corrections by demonstrating that Regge behavior—characteristic of string scattering at high energies—suppresses the problematic time delays. Using tree-level and loop amplitudes in bosonic string theory, it shows that full string dynamics, including infinite-spin Regge trajectories, naturally avoid the acausal effects predicted in effective field theory approximations.

ABSTRACT

Higher-derivative corrections to the Einstein-Hilbert action are present in bosonic string theory leading to the potential causality violations recently pointed out by Camanho et al. We analyze in detail this question by considering high-energy string-brane collisions at impact parameters $b \le l_s$ (the string-length parameter) with $l_s \gg R_p$ (the characteristic scale of the D$p$-brane geometry). If we keep only the contribution of the massless states causality is violated for a set of initial states whose polarization is suitably chosen with respect to the impact parameter vector. Such violations are instead neatly avoided when the full structure of string theory - and in particular its Regge behavior - is taken into account.

Motivation & Objective

• To resolve causality violations in effective field theories with higher-derivative gravity corrections, as identified by Camanho et al. (CEMZ).
• To investigate whether full string theory, particularly its Regge behavior, can resolve these violations where effective field theory fails.
• To analyze high-energy string-brane scattering in the bosonic string theory framework, focusing on the $b \ll l_s$ regime and small string coupling.
• To establish a connection between the eikonal phase in string theory and the Shapiro time delay, showing how string dynamics restore causality.

Proposed method

• Derive tree-level string scattering amplitudes for a massless string state (graviton, dilaton, or Kalb-Ramond field) scattering off a stack of $N \gg 1$ D$p$-branes in the critical bosonic string theory.
• Analyze the Regge asymptotics of the amplitude, focusing on the high-energy, fixed-angle limit where string Regge trajectories dominate.
• Use operator eikonal exponentiation at the annulus level to derive a unitary S-matrix in the large-$N$ limit, analogous to the eikonal phase in effective field theory.
• Compare the resulting eikonal phase to the effective field theory result, identifying the Shapiro time delay via $\Delta t = 2\partial_E \delta(E,b)$.
• Compute the metric of a D$p$-brane stack in $d$ dimensions and derive the Shapiro time delay in the weak-field, large-impact-parameter limit.
• Contrast the field-theory result (with $R^2$, $R^3$ corrections) showing sign-flipped time delays for certain polarizations with the string-theory result, where Regge behavior cancels the acausal effects.

Experimental results

Research questions

• RQ1 Can higher-derivative gravity corrections in effective field theory lead to causality violations in high-energy scattering, as suggested by CEMZ?
• RQ2 Does the full structure of string theory—specifically its Regge behavior—resolve the causality violations predicted in effective field theory approximations?
• RQ3 How does the eikonal phase in string theory differ from that in effective field theory when $b \ll l_s$ and $R_p \ll l_s$?
• RQ4 What role do infinite-spin Regge trajectories play in restoring causality in string theory?
• RQ5 Can the Shapiro time delay in string-brane scattering be computed consistently in the full string framework, and does it avoid the sign flip seen in effective field theory?

Key findings

• The effective field theory limit of string theory—specifically the bosonic string with $R^2$ and $R^3$ corrections—exhibits causality violations via negative Shapiro time delays for certain polarizations, as predicted by CEMZ.
• In the full string theory, the Regge behavior of the scattering amplitude ensures that the time delay remains positive and causal, even at $b \ll l_s$, by suppressing the problematic higher-derivative contributions.
• The eikonal phase derived from string amplitudes at the annulus level reproduces the correct causal time delay, with $\Delta t = 2\partial_E \delta(E,b)$ matching the field-theory result only when Regge behavior is included.
• The infinite tower of higher-spin states in string theory, encoded in the Regge trajectory, is essential for restoring causality and preventing acausal signal propagation.
• The time delay in the string theory framework is given by $\Delta t = \frac{R_p^{d-p-3} \sqrt{\pi} \Gamma(\frac{d-p-4}{2})}{2 b^{d-p-4} \Gamma(\frac{d-p-3}{2})}$, which remains positive and causal, in contrast to the sign-flipped result in the effective field theory.
• The resolution of causality violations is not due to a cancellation of terms, but due to the non-perturbative structure of string amplitudes, particularly the Regge limit behavior, which modifies the high-energy dynamics fundamentally.