_________________________________________________________________________Swansea University E-Theses D-brane sources in supergravity and gauge/string duality at finite temperature. Schmude, Johannes How to cite: _________________________________________________________________________ Schmude, Johannes (2010) D-brane sources in supergravity and gauge/string duality at finite temperature.. thesis, Swansea University. http://cronfa.swan.ac.uk/Record/cronfa43146 Use policy: _________________________________________________________________________ This item is brought to you by Swansea University. Any person downloading material is agreeing to abide by the terms of the repository licence: copies of full text items may be used or reproduced in any format or medium, without prior permission for personal research or study, educational or non-commercial purposes only. The copyright for any work remains with the original author unless otherwise specified. The full-text must not be sold in any format or medium without the formal permission of the copyright holder. Permission for multiple reproductions should be obtained from the original author. Authors are personally responsible for adhering to copyright and publisher restrictions when uploading content to the repository. Please link to the metadata record in the Swansea University repository, Cronfa (link given in the citation reference above.) http://www.swansea.ac.uk/library/researchsupport/ris-support/ I p a d c K / S/n D-brane sources in supergravity and gauge/string duality at finite temperature Johannes Schmude Submitted to the University of Wales in fulfilment of the requirements for the degree of Doctor of Philosophy SWANSEA UNIVERSITY LIBRARY NOT TO BE REMOVED PROM THE LIBRARY Swansea University 2010 ProQuest Number: 10821538 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a com plete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. uest ProQuest 10821538 Published by ProQuest LLC(2018). Copyright of the Dissertation is held by the Author. All rights reserved. This work is protected against unauthorized copying under Title 17, United States C ode Microform Edition © ProQuest LLC. ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 48106- 1346 A b stra ct This thesis deals with two independent aspects of gauge/string duality: The in­ clusion of fundamental matter in string duals via backreaction and the study of quark-gluon plasma physics using the duality. Concerning the flavoring proce­ dure, we focus on the role of source terms for D-branes. Here, we are especially interested in various technical issues such as the construction of suitable source densities, their relation to generalized calibrated geometry and the M-theory lift of such sources in the special case where these appear as smeared KK-monopoles. In this context we will study several examples of flavored supergravity du­ als, such as the flavored Maldacena-Nunez and Klebanov-Witten solutions, and further examples based on D5-D5, D6-D6 and D3-D7 intersections in 2+1 and 3+1 dimensions, all of which preserve some supersymmetry. The parts focussing on QGP physics will exhibit an attempt at construct­ ing a type IIA background based on D6-branes wrapped on three-cycles that is dual to a super Yang-Mills theory with four supercharges at finite temperature. Studying thermodynamic properties, deconfinement as well as parton energy loss, we come to the puzzling conclusion that the standard approach to con­ structing such a solution does not provide the searched for dual. We are able to give some explanation for this by comparing the eleven-dimensional background with the Schwarzschild and Reissner-Nordstrom black holes in four dimensions. r ( LIBRARY Declaration This work has not previously been accepted in substance for any degree and is not being concurrently submitted in candidature for any degree. Signed (candidate) Date First statement This thesis is the result of my own investigations, except where otherwise stated. Where correction services have been used, the extent and nature of the correc­ tion is clearly marked in a footnote(s). Other sources are acknowledged by endnotes giving explicit references. A bib­ liography is appended. Signed (candidate) Date ___________ Second statement I hereby give consent for my thesis, if accepted, to be available for photocopying and for inter-library loan, and for the title and abstract to be made available to outside organisations. Signed _ (candidate) Date f t Contents 1 Introduction 7 1.1 Flavors and D-brane sources ............................... 7 1.2 Quark-gluon plasma physics ...................................................................... 13 2 D-brane sources in supergravity 15 2.1 The supergravities ....................................................................................... 15 2.2 1/2-BPS branes in flat space ................................................................... 19 2.3 Supersyinmetric branes ............................................................................. 24 3 Geometric aspects 29 3.1 The geometry of smeared branes ............................................................ 30 3.1.1 Three examples ................................................................................ 30 3.1.2 The generic c a se ............................................................................. 47 3.2 Af = 2 gauge-string duality in d — 2 + 1 .............................................. 51 3.2.1 The unflavored solution ............................................................... 51 3.2.2 Deformation of the solution ........................................................ 53 3.2.3 Calibration, smearing and G-structures ................................ 53 3.2.4 Addition and smearing of flavor branes .................................... 57 3.3 Discussion ............................................................................................. 61 3.A Finding the calibration form - an explicit exam ple ......................... 62 4 Color- vs. flavor-branes 66 4.1 General rem arks .......................................................................................... 67 4.2 D3-D7 solutions .............................................................................................. 68 4.2.1 An aside: T-dualities ...................................................................... 70 4.2.2 Simple, known solutions ............................................................... 71 4.2.3 Analytic solutions ......................................................................... 72 4.2.4 Brane distributions .......................................................................... 74 4.2.5 Numeric solutions ......................................................................... 75 4.3 Discussion ........................................................................................................ 79 5 Kaluza-Klein monopole condensation 81 5.1 Flavored Af = 1 string duals from D6-branes ....................................... 86 5.1.1 The eleven-dimensional dual without sources ...................... 87 5.1.2 Smeared sources in type IIA supergravity ............................. 92 5.1.3 Finding a solution ......................................................................... 95 5.2 Back to M-theory ......................................................................... 97 5.2.1 Lifting the SUSY variations ........................................................ 97 1 5.2.2 The equations of m otion ...................................................................100 5.3 Discussion ..........................................................................................................106 5.A D6-brane embeddings ..................................................................................108 5.B Kaluza-Klein reduction of supergravity variations with torsion . Ill 6 The duality at finite temperature 116 6.1 The supergravity dual at zero temperature ............................................118 6.1.1 M-theory on the holonomy manifold ....................................118 6.1.2 Wrapped D6-branes in type IIA string theory ......................... 119 6.2 The gauge theory at zero temperature .....................................122 6.2.1 The coupling constant of the gauge theory ................................ 122 6.2.2 Field Content ........................................................................................124 6.2.3 The gauge/gravity correspondence .............................................. 125 6.2.4 Wilson loops and minimal surfaces .............................................. 126 6.2.5 The quark-antiquark potential & confinement ..........................129 6.3 The supergravity theory at finite temperature .....................................134 6.3.1 The eleven-dimensional black h o le .............................................. 134 6.3.2 Thermodynamics .................................................................................135 6.3.3 Comparison with the Schwarzschild solution .............................140 6.3.4 Dimensional Reduction ................................................................... 141 6.4 The field theory at finite temperature ...................................................142 6.4.1 Properties of the Dual Field T heory