Abstract
We study rigidly rotating and pulsating (m, n) strings in AdS_3 times S^3 with mixed three form flux. The AdS_3 times S^3 background with mixed three form flux is obtained in the near horizon limit of SL(2, Z)-transformed solution, corresponding to the bound state of NS5-branes and fundamental strings. We study the probe (m, n)-string in this background by solving the manifest SL(2, Z)-covariant form of the action. We find the dyonic giant magnon and single spike solutions corresponding to the equations of motion of a probe string in this background and find various relationships among the conserved charges. We further study a class of pulsating (m, n) string in AdS_3 with mixed three form flux.
Highlights
Integrability in string theory has been proved to be one of the most useful techniques in studying the string spectrum in various semisymmetric superspaces [1].1 The appearance of integrability on both sides of the AdS/CFT correspondence [3,4,5] has led to tremendous progress in the study of string theory
Schwarz [15] has constructed an SL(2, Z ) multiplet of string-like solutions in type IIB string theory starting from the fundamental string solution
We see that we reduced the problem of the dynamics of the (m, n)-string in mixed Ad S3 × S3 background to the much simpler analysis of (m, n )-string in pure NS–NS Ad S3 × S3 background where the action is given in (13)
Summary
Integrability in string theory has been proved to be one of the most useful techniques in studying the string spectrum in various semisymmetric superspaces [1].1 The appearance of integrability on both sides of the AdS/CFT correspondence [3,4,5] has led to tremendous progress in the study of string theory. It is well known that the equations of motion of type IIB supergravity theory are invariant under an SL(2, R) group This suggests the possibility to generate new supergravity solutions by applying this rotation to known solutions such as string-like as well as five-brane solutions. Note that this action is expressed using the Einstein frame metric gM N , which is related to the string frame metric G M N by the relation gM N = e− /2G M N where the Einstein frame metric is invariant under SL(2, Z )-transformations It was shown in [30] that the (m, n)-string in a mixed Ad S3×S3 background with mixed three form fluxes can be mapped to an (m , n )-string in an Ad S3 × S3 background with NS–NS three form flux. Before we proceed to the discussion of the general case with two angular momenta, we consider the simpler case of single angular momentum
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