Dual Purpose Landscaping Tools: Small Extra Dimensions in AdS/CFT

We propose a class of AdS/CFT dual pairs which have small internal dimensions on the gravity side. Starting from known Freund-Rubin AdS/CFT dual pairs, we use 7-branes to nearly cancel the curvature energy of the internal dimensions while maintaining their stabilization. This leads to a new corner of the landscape - a class of AdS solutions with a hierarchically large AdS radius - with a dual field theory given (implicitly) by the infrared limit of a concrete brane construction involving D3-branes, 7-branes, and curvature. We first construct a class of hierarchical AdS5/CFT4 dual pairs with a simple formula for the number of degrees of freedom which we interpret in the dual QFT. We then generalize these to AdS4/CFT3 duals, and suggest extensions of the method to obtain de Sitter solutions.

[1]  A. Polyakov,et al.  Gauge Theory Correlators from Non-Critical String Theory , 1998, hep-th/9802109.

[2]  S. Kachru,et al.  Fixing all moduli in a simple f-theory compactification , 2005, hep-th/0503124.

[3]  Yaron E. Antebi,et al.  On the conformal field theory duals of type IIA AdS 4 flux compactifications , 2008, 0801.3326.

[4]  J. Maldacena.  The Large-N Limit of Superconformal Field Theories and Supergravity , 1997, hep-th/9711200.

[5]  A. Sen.  F-theory and orientifolds , 1996, hep-th/9605150.

[6]  AdS and dS Entropy from String Junctions , 2003, hep-th/0308175.

[7]  On the Landau-Ginzburg description of N=2 minimal models , 1993, hep-th/9304026.

[8]  J. Maldacena,et al.  The gravity duals of N=2 superconformal field theories , 2009, 0904.4466.

[9]  E. Witten,et al.  New N= 2 superconformal field theories in four dimensions , 1995, hep-th/9511154.

[10]  Brane dimers and quiver gauge theories , 2005, hep-th/0504110.

[11]  4D Conformal Field Theories and Strings on Orbifolds , 1998, hep-th/9802183.

[12]  S. Kachru,et al.  Physics of String Flux Compactifications , 2007, hep-th/0701050.

[13]  L. Motl,et al.  The String landscape, black holes and gravity as the weakest force , 2006, hep-th/0601001.

[14]  TASI/PiTP/ISS Lectures on Moduli and Microphysics , 2004, hep-th/0405068.

[15]  Holographic framework for eternal inflation , 2006, hep-th/0606204.

[16]  D. Freedman,et al.  Stability in Gauged Extended Supergravity , 1982 .

[17]  F. Denef.  Les Houches Lectures on Constructing String Vacua , 2008, 0803.1194.

[18]  V. Balasubramanian,et al.  Systematics of moduli stabilisation in Calabi-Yau flux compactifications , 2005, hep-th/0502058.

[19]  Compactifications of F-Theory on Calabi--Yau Threefolds -- I , 1996, hep-th/9602114.

[20]  M. Graña.  Flux compactifications in string theory: A Comprehensive review , 2005, hep-th/0509003.

[21]  E. Silverstein,et al.  A new handle on de sitter compactifications , 2004, hep-th/0411271.

[22]  J. Maldacena,et al.  N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals , 2008, 0806.1218.

[23]  Edward Witten,et al.  Phases of N = 2 theories in two dimensions , 1993, hep-th/9301042.

[24]  D. Waldram,et al.  Sasaki-Einstein Metrics on S^2 x S^3 , 2004 .

[25]  Shamit Kachru,et al.  De Sitter vacua in string theory , 2003, hep-th/0301240.

[26]  Kristian D. Kennaway,et al.  Dimer models and toric diagrams , 2005, hep-th/0503149.

[27]  Auto-localization in de-Sitter space , 2003, hep-th/0305192.

[28]  A. U.S.,et al.  Type IIA Moduli Stabilization , 2005 .

[29]  S. Kachru,et al.  Conformal Theories and Strings on Orbifolds , 1998 .

[30]  Gauge theories from toric geometry and brane tilings , 2005, hep-th/0505211.

[31]  E. Witten.  Anti-de Sitter space and holography , 1998, hep-th/9802150.

[32]  The Large N Limit of ${\cal N} =2,1 $ Field Theories from Threebranes in F-theory , 1998, hep-th/9806159.

[33]  New Phenomena in SU(3) Supersymmetric Gauge Theory , 1995, hep-th/9505062.

[34]  M theory as a matrix model: A Conjecture , 1996, hep-th/9610043.

[35]  Warped Strings: Self-dual Flux and Contemporary Compactifications , 2003, hep-th/0308156.

[36]  R. Bousso.  TASI Lectures on the cosmological constant , 2008 .

[37]  E. Witten.  ANTI-DE SITTER SPACE, THERMAL PHASE TRANSITION AND CONFINEMENT IN GAUGE THEORIES , 1998, hep-th/9803131.

[38]  E. Silverstein.  AdS and dS Entropy from String Junctions or The Function of Junction Conjunctions 1 , 2003 .

[39]  E. Witten,et al.  Superconformal field theory on threebranes at a Calabi-Yau singularity , 1998, hep-th/9807080.

[40]  Hierarchies from fluxes in string compactifications , 2001, hep-th/0105097.

[41]  C. Vafa.  Evidence for F theory , 1996, hep-th/9602022.

[42]  The dS/dS Correspondence , 2004, hep-th/0407125.

[43]  S. Franco,et al.  An Infinite Family of Superconformal Quiver Gauge Theories with Sasaki-Einstein Duals , 2004, hep-th/0411264.

[44]  Flux Compactification , 2006, hep-th/0610102.

[45]  The Cosmological Constant and the String Landscape , 2006, hep-th/0603249.

[46]  M. Bershadsky.  Compactifications of F-theory , 1998 .

[47]  New Einstein-Sasaki and Einstein Spaces from Kerr-de Sitter , 2005, hep-th/0505223.