On D-brane configurations and ADS/CFT duality

Resumo

String theory has been a considerable conceptual and mathematical advance in the search for the most fundamental theory of physics. The idea started in the 1960's, by considering the smaller constituents of matter as one-dimensional objects represented by vibrant strings, in an attempt to describe the strong interaction. The attempt failed, but years later, string theory was recovered and has been developed as a possible unification theory in which numerous advances continue to take place nowadays, and which would encompass all known matter particles and interactions. In this thesis two independent research works in the area of string theory are presented. The first one falls in the context of the unstable non-BPS configurations, while the other has to do with the particle-like branes appearing in relation to the AdS/CFT conjecture. After a general introductory chapter to the strings, branes and dualities, each research work appears in a separate part of the thesis (parts I, II). Conclusions are given at the end of each part. In the first part we introduce certain unstable non-BPS brane configurations, the non-BPS Dp-branes and the (Dp,anti-Dp) systems. Their instability is reflected in the presence of tachyonic modes in their string spectra. These tachyonic modes can decay (`condense') giving rise to a new configuration, which can in turn be stable or not. The boundary state formalism is introduced, as well as an effective potential approach, in order to tackle the problem and lay the basis for the research work presented in this first part. That research is presented as an adaptation of [1]. In this work we present a worldvolume effective action suitable for the study of the confined phase of a (Dp,anti-Dp) system at weak coupling. We identify the mechanism by which the fundamental string arises from this action when the Dp and the anti-Dp annihilate. We also construct an explicit dual action, more suitable for the study of the strong coupling regime. Our dual description indicates that the condensing tachyonic objects originate from open D(p-2)-branes stretched between the brane and the antibrane. In the second part of the thesis we present the most relevant results from the particle-like branes appearing in relation to AdS/CFT. These configurations are made of branes living in the bulk of AdS and a certain number strings stretched all the way to the boundary, where they are seen as external quarks. We review the stability study of the baryon vertex in the AdS5 x S5 background and how this configuration was generalized by introducing a magnetic flux. We also comment on the Di-baryon configurations that appear in the same context. Finally and before presenting [2], we explain the basis of the ABJM theory, an AdS/CFT proposal realized over an AdS4 space and related to a three dimensional supersymmetric Chern-Simons matter theory. In [2] we study the effect of adding lower dimensional brane charges, generalizing the particle-like brane configurations that appears in AdS4 x P3. We show that these configurations require additional fundamental strings in order to cancel certain worldvolume tadpoles appearing. A dynamical study reveals that the charges must lie inside some interval in order to find well defined configurations, and for the baryon vertex and the di-baryon, the number of fundamental strings must also lie inside an allowed interval. We also discuss how these configurations are modified in the presence of a non-zero Romans mass. [1] N. Gutierrez, Y. Lozano, Phys. Rev. D79 (2009) 046010, arXiv:0809.1005 [hep-th] [2] N. Gutierrez, Y. Lozano, D. Rodriguez-Gomez, JHEP 1009 (2010) 101, arXiv:1004.2826 [hep-th].