Gravity, thermodynamics and cosmology

Lead Research Organisation: University of Edinburgh
Department Name: Sch of Mathematics

Abstract

There are two types of fundamental forces in Nature: those responsible for particle interactions at subatomic scales and those responsible for the large scale structure of the universe. The latter is described by Einstein's General Theory of Relativity (GR) and the former by Quantum Field Theories (QFTs) such as the Standard Model. Einstein's theory is conceptually simple, but is classical and breaksdown when the force of gravity is strong, as it is at very small scales, whereas QFTs are effective theories which ignore the gravitational interactions and which cannot be trusted at very high energies. During the last three decades, String Theory has emerged as a conceptually rich theoretical framework reconciling both GR and QFT. In particular, it is a theory of quantum gravity and my research programme is firmly focused on a wide range of quantum gravitational aspects of String Theory.String theory challenges the geometrical notions of spacetime on which GR is predicated. At very small( stringy ) scales the nature of spacetime is believed to be fundamentally different from GR---its continuous structures thought to be replaced by discrete, algebraic structures. Black holes are ideal candidates to study this transition. They are thermodynamical objects allowing a classical description in terms of Einstein's equations. Just as a gas allows a thermodynamical description in terms of temperature, pressure and volume, but it also has a description in terms of statistical properties of its constituent molecules, I look for the atoms of spacetime responsible for the entropy of the black holes. I plan to extend our current understanding on supersymmetric black holes, to less supersymmetric systems, and eventually to non-supersymmetric, and thus more realistic, ones. Any progress in the latter direction would be of extraordinary importance in our field.The expansion of the universe is incontrovertible. Since its creation after the Big Bang, the universe has been in permanent evolution. One may wonder whether a physical test of string theory will come from the realm of cosmology. I propose to study both theoretical and experimental aspects of this expectation. At a formal level, I want to develop the poorly understood string theory tools to deal with these physical situations in order to be able to answer questions such as Does string theory resolve Big-Bang-type singularities? ---a natural question in view of the fact that string theory is known to resolve other types ofsingularities. I also want to explore whether our ideas on black holes can help us understand the potential thermodynamical nature of the universe accessible to a classical observer. At an experimental level, I want to derive observable cosmological consequences of string theory in an effort to falsify it or at least to constraint the landscape of possible vacua explaining the universe we live in.The main beneficiaries from my work would be the members of the scientific community working on related topics to the ones developed in this proposal : cosmology & astrophysics, QFT, GR, stringtheory, statistical mechanics, information theory and mathematical physics. Any human being interested in knowing about the structure of the world in which we live, both from the measurable point of view, but also from a much more conceptual point of view, would find my work of interest.

Publications

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Bagchi A (2013) Holography of 3D flat cosmological horizons. in Physical review letters

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Balasubramanian V (2011) Helical Luttinger liquids and three-dimensional black holes in Physical Review D

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Balasubramanian V (2010) What is a chiral 2d CFT? And what does it have to do with extremal black holes? in Journal of High Energy Physics

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Balasubramanian V (2013) A strongly coupled zig-zag transition in Journal of High Energy Physics

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Balasubramanian V (2014) Black holes, entanglement and random matrices in Classical and Quantum Gravity

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Castro A (2009) Deconstructing the D0-D6 system in Journal of High Energy Physics

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De Boer J (2011) Near-horizon limits of massless BTZ and their CFT duals in Classical and Quantum Gravity

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De Boer J (2012) Emergent IR dual 2d CFTs in charged AdS 5 black holes in Physical Review D

 
Description Since the start of the First grant in March 2009, I would divide my main findings in three big categories : the physics of extremal black holes, the application of string theory to cosmology and the application of holography ideas to flat space and strongly coupled condensed matter systems.In the context of black holes, I have a constituent model for certain extremal non-supersymmetric ones explaining their main macroscopic properties. This is analogous to identifying the "molecules" of a gas in a room for these gravitational objects. Furthermore, I showed that the quantum dynamics of these "molecules" is governed by a very specific set of quantum field theories : two dimensional chiral conformal field theories (CFTs). I showed these arise as infinite momentum limits of standard non-chiral CFTs used in statistical mechanics and condensed matter. I have made these discussions very precise when these black holes are small.In the context of cosmology, I developed a computer algorithm to identify the subset of spaces where to compactify string theory to connect it to the real world. The main constraint used so far is to make sure such space allows a vacuum compatible with what we see without going beyond the regime of validity of the methods being used. These results have triggered a better analytical description of the mathematical properties these spaces require.In the context of holography, I have explored the use of the famous Anti deSitter-CFT correspondence conjectured in string theory to describe strongly coupled real laboratory systems such as Luttinger liquids, including their interactions with fermions. I have definite statements regarding the stability of these systems and their phase space structure as a function of the different physical parameters. Furthermore, I have proposed some preliminary extension of these holographic ideas to flat space, by identifying what the relevant symmetries are and what kind of quantum mechanical theories realise them.
Exploitation Route My findings can be directly used by the theoretical community I belong to. There are many scientific papers that build on my results, as one can check by reading the references that have cited my work. In particular, my work on extremal black holes and its connection to chiral CFTs was internationally appreciated and my recent work in flat holography opens new venues to attack this difficult conceptual problem.
Sectors Other

 
Description My findings have been used academically. My work on strongly coupled condensed matter systems and its explicit predictions may be experimentally tested on a lab.
First Year Of Impact 2010
Sector Other
Impact Types Cultural

 
Description Extremal Black Holes 
Organisation School of Physics; Institute for Research in Fundamental Sciences
Country Iran, Islamic Republic of 
Sector Academic/University 
PI Contribution Holographic description of certain extremal black holes and their universal thermodynamic relations consistent with it
Collaborator Contribution Classification of different extremal behaviour compatible with vanishing black hole horizon size
Impact What is a 2d chiral CFT ? and what does it have to do with extremal black holes ?, J. High Energy Phys. 02 (2010) 017. Near horizon limits of massless BTZ and their CFT duals, Class. Quantum Grav. 28 (2011) 175012 . Emergent IR dual 2d CFTs in charged AdS$_5$ black holes, Phys. Rev D85, 084039 (2012). Near-Extremal Vanishing Horizon AdS_5 Black Holes and Their CFT Duals, J. High Energy Phys. 1304 (2013) 045. Extremal black holes and first law of thermodynamics, Phys. Rev. D88, 101503 (2013).
Start Year 2010
 
Description Flat holography 
Organisation Vienna University of Technology
Country Austria 
Sector Academic/University 
PI Contribution The understanding of solutions to 3d pure gravity as lorentzian orbifolds and their global structures
Collaborator Contribution The study and relevance of boundary conditions to set up consistent variational principles
Impact two scientific papers : 1. Cosmic evolution from phase transition of 3-dimensional flat space, Phys. Rev. Lett. 111, 181301 (2013). 2. Variational principle and 1-point functions in 3 dimensional flat space Einstein gravity, Phys. Rev. D89 084061 (2014).
Start Year 2012
 
Description Swiss Cheese 
Organisation City, University of London
Department Department of Mathematics
Country United Kingdom 
Sector Academic/University 
PI Contribution Analytic description of solutions leading to large volume CY compactifications
Collaborator Contribution Computer coding to determine the existence of such compactifications in large data sets of known Calabi-Yau manifolds
Impact Calabi-Yau manifolds with large volume vacua, Phys. Rev. D86, 101901 (1012).
Start Year 2011
 
Description Swiss Cheese 
Organisation Northeastern University - Boston
Department Department of Physics
Country United States 
Sector Academic/University 
PI Contribution Analytic description of solutions leading to large volume CY compactifications
Collaborator Contribution Computer coding to determine the existence of such compactifications in large data sets of known Calabi-Yau manifolds
Impact Calabi-Yau manifolds with large volume vacua, Phys. Rev. D86, 101901 (1012).
Start Year 2011
 
Description Swiss Cheese 
Organisation University of the Witwatersrand
Country South Africa 
Sector Academic/University 
PI Contribution Analytic description of solutions leading to large volume CY compactifications
Collaborator Contribution Computer coding to determine the existence of such compactifications in large data sets of known Calabi-Yau manifolds
Impact Calabi-Yau manifolds with large volume vacua, Phys. Rev. D86, 101901 (1012).
Start Year 2011
 
Description Swiss Cheese 
Organisation Virginia Tech
Country United States 
Sector Academic/University 
PI Contribution Analytic description of solutions leading to large volume CY compactifications
Collaborator Contribution Computer coding to determine the existence of such compactifications in large data sets of known Calabi-Yau manifolds
Impact Calabi-Yau manifolds with large volume vacua, Phys. Rev. D86, 101901 (1012).
Start Year 2011