Abstract

We consider string pair production in non homogeneous electric backgrounds. We study several particular configurations which can be addressed with the Euclidean world-sheet instanton technique, the analogue of the world-line instanton for particles. In the first case the string is suspended between two D-branes in flat space-time, in the second case the string lives in AdS and terminates on one D-brane (this realizes the holographic Schwinger effect). In some regions of parameter space the result is well approximated by the known analytical formulas, either the particle pair production in non-homogeneous background or the string pair production in homogeneous background. In other cases we see effects which are intrinsically stringy and related to the non-homogeneity of the background. The pair production is enhanced already for particles in time dependent electric field backgrounds. The string nature enhances this even further. For spacial varying electrical background fields the string pair production is less suppressed than the rate of particle pair production. We discuss in some detail how the critical field is affected by the non-homogeneity, for both time and space dependent electric field backgrouds. We also comment on what could be an interesting new prediction for the small field limit. The third case we consider is pair production in holographic confining backgrounds with homogeneous and non-homogeneous fields.

Highlights

  • In this paper we consider the pair production in string theory for non-homogeneous backgrounds

  • In this paper we studied string pair production in non-homogeneous electric backgrounds using the instanton technique

  • 4K and E are complete elliptic integrals of first and second kind. By this method, strings suspended between two separated D-branes in flat space-time, and the holographic Schwinger effect

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Summary

Particle pair production

We review the main results of the world-line instanton technique applied to the study of the particle pair production [18, 19]. We turn to show how these results affects the pair production rate in the different cases These rates depend on the actions of the instanton solution. In the left panel we compare the constant background solution with the pulse and oscillatory temporal backgrounds Both curves are below the constant background one, indicating an enhancement in the pair production probability ∝ e−SE. When there is no time dependence, pair production is just a tunneling event Since this event is non-local, the pair production is suppressed with respect to a constant field equal to the maximum value. We have a mixture between tunneling and energy absorption: the particles can absorb energy from the background field This is responsible for the enhancement of the pair production

String pair production: flat space
String pair production: holography
Findings
Conclusions and open issues
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