Topologically massive higher- spin gravity Bindusar Sahoo Nikhef - PowerPoint PPT Presentation

Topologically massive higher- spin gravity Bindusar Sahoo Nikhef theory group Amsterdam IOP Bhubaneswar 1st March 2013 1

Topologically massive higher- spin gravity Bindusar Sahoo Nikhef theory group Amsterdam IOP Bhubaneswar 1st March 2013 ★ Arjun Bagchi, Shailesh Lal, Arunabha Saha and BS, “T opologically Massive Higher Spin Gravity,” [ arXiv:1107.0915[hep- th]], JHEP 1110 (2011) 150 ★ Arjun Bagchi, Shailesh Lal, Arunabha Saha and BS, “One loop partition function for T opologically Massive Higher Spin Gravity,” [ arXiv:1107.2063[hep-th]], JHEP 1112 (2011) 068 1

Plan of talk 2

Plan of talk • General introduction and motivation 2

Plan of talk • General introduction and motivation • Introduction and overview of higher-spin theories 2

Plan of talk • General introduction and motivation • Introduction and overview of higher-spin theories • Introduction and overview of topologically massive gravity 2

Plan of talk • General introduction and motivation • Introduction and overview of higher-spin theories • Introduction and overview of topologically massive gravity • Classical aspects of topologically massive higher-spin gravity 2

Plan of talk • General introduction and motivation • Introduction and overview of higher-spin theories • Introduction and overview of topologically massive gravity • Classical aspects of topologically massive higher-spin gravity • One loop partition function 2

Plan of talk • General introduction and motivation • Introduction and overview of higher-spin theories • Introduction and overview of topologically massive gravity • Classical aspects of topologically massive higher-spin gravity • One loop partition function • Future directions 2

General Introduction and Motivation 3

General Introduction and Motivation Understanding the quantum nature of gravity is very crucial 3

General Introduction and Motivation Understanding the quantum nature of gravity is very crucial The appropriate degrees of freedom required to formulate quantum gravity resides in one less spatial dimension - Holographic Principle • G. ’t Hooft, gr-qc/9310026. • L. Susskind, J. Math. Phys. 36, 6377 (1995) [hep-th/9409089] 3

General Introduction and Motivation • In the context of string theory holographic principle is realized via the celebrated AdS-CFT Conjecture, J. M. Maldacena, Adv. Theor. Math. Phys. 2 (1998) 231 [hep-th/9711200] 4

General Introduction and Motivation • In the context of string theory holographic principle is realized via the celebrated AdS-CFT Conjecture, J. M. Maldacena, Adv. Theor. Math. Phys. 2 (1998) 231 [hep-th/9711200] • It relates string theory/(super)gravity theory on negatively curved anti-de Sitter (AdS) spacetime to a (super) conformal field theory (CFT) on the boundary of the AdS space-time. 4

General Introduction and Motivation • In the context of string theory holographic principle is realized via the celebrated AdS-CFT Conjecture, J. M. Maldacena, Adv. Theor. Math. Phys. 2 (1998) 231 [hep-th/9711200] • It relates string theory/(super)gravity theory on negatively curved anti-de Sitter (AdS) spacetime to a (super) conformal field theory (CFT) on the boundary of the AdS space-time. 4

General Introduction and Motivation • In the context of string theory holographic principle is realized via the celebrated AdS-CFT Conjecture, J. M. Maldacena, Adv. Theor. Math. Phys. 2 (1998) 231 [hep-th/9711200] • It relates string theory/(super)gravity theory on negatively curved anti-de Sitter (AdS) spacetime to a (super) conformal field theory (CFT) on the boundary of the AdS space-time. ⌧ � Z exp = Z s ( φ 0 ) φ 0 O CF T Edward Witten, Adv.Theor.Math.Phys. 2 (1998) 253-291 [hep-th/9802150 ] 4

General Introduction and Motivation 5

General Introduction and Motivation • Applications of AdS-CFT is limited to understanding strongly coupled gauge theories from gravity 5

General Introduction and Motivation • Applications of AdS-CFT is limited to understanding strongly coupled gauge theories from gravity • Hydrodynamics 5

General Introduction and Motivation • Applications of AdS-CFT is limited to understanding strongly coupled gauge theories from gravity • Hydrodynamics • QCD 5

General Introduction and Motivation • Applications of AdS-CFT is limited to understanding strongly coupled gauge theories from gravity • Hydrodynamics • QCD • Condensed matter physics 5

General Introduction and Motivation • Applications of AdS-CFT is limited to understanding strongly coupled gauge theories from gravity • Hydrodynamics • QCD • Condensed matter physics • Very little progress in understanding quantum gravity from CFT 5

General Introduction and Motivation • Applications of AdS-CFT is limited to understanding strongly coupled gauge theories from gravity • Hydrodynamics • QCD • Condensed matter physics • Very little progress in understanding quantum gravity from CFT • It involves finding CFT duals with analytic tractability and intrinsic complexity so that one is able to capture some aspects of quantum gravity with quantitative precision 5

General Introduction and Motivation • Applications of AdS-CFT is limited to understanding strongly coupled gauge theories from gravity • Hydrodynamics • QCD • Condensed matter physics • Very little progress in understanding quantum gravity from CFT • It involves finding CFT duals with analytic tractability and intrinsic complexity so that one is able to capture some aspects of quantum gravity with quantitative precision • There are problems connecting AdS-CFT to the real world because it relies on supersymmetry and cannot be defined on de Sitter spacetime 5

General Introduction and Motivation • Applications of AdS-CFT is limited to understanding strongly coupled gauge theories from gravity • Hydrodynamics • QCD • Condensed matter physics • Very little progress in understanding quantum gravity from CFT • It involves finding CFT duals with analytic tractability and intrinsic complexity so that one is able to capture some aspects of quantum gravity with quantitative precision • There are problems connecting AdS-CFT to the real world because it relies on supersymmetry and cannot be defined on de Sitter spacetime Higher Spin holography helps !! 5

Introduction and overview of higher-spin theories in three dimensions • Higher-spin theories are gravitational theories in the presence of additional higher-spin (s>2) gauge field 6

Introduction and overview of higher-spin theories in three dimensions • Higher-spin theories are gravitational theories in the presence of additional higher-spin (s>2) gauge field • Theories of this type were first constructed by Vasiliev for [ M.A. Vasiliev, Int. J. AdS 4 Mod. Phys. A 6 (1991) 1115 ] and were later generalized to AdS 3 6

Introduction and overview of higher-spin theories in three dimensions • Higher-spin theories are gravitational theories in the presence of additional higher-spin (s>2) gauge field • Theories of this type were first constructed by Vasiliev for [ M.A. Vasiliev, Int. J. AdS 4 Mod. Phys. A 6 (1991) 1115 ] and were later generalized to AdS 3 • Unlike their higher-dimensional cousins, they admit a truncation to an arbitrary maximal spin N, rather than involving the customary infinite tower of higher-spin fields 6

Introduction and overview of higher-spin theories in three dimensions • Higher-spin theories are gravitational theories in the presence of additional higher-spin (s>2) gauge field • Theories of this type were first constructed by Vasiliev for [ M.A. Vasiliev, Int. J. AdS 4 Mod. Phys. A 6 (1991) 1115 ] and were later generalized to AdS 3 • Unlike their higher-dimensional cousins, they admit a truncation to an arbitrary maximal spin N, rather than involving the customary infinite tower of higher-spin fields • Essentially they can be written as a SL ( N , R ) × SL ( N , R ) gauge theory as: 6

Introduction and overview of higher-spin theories in three dimensions ` ` 16 ⇡ GS CS [ ˜ S = 16 ⇡ GS CS [ A ] − A ] ✓ ◆ A ∧ dA + 2 Z S CS [ A ] = tr 3 A ∧ A ∧ A � � A = j a µ J a + t a 1 ··· a s − 1 T a 1 ··· a s − 1 dx µ µ ⌘ a ⌘ a ! + e ! − e ⇣ ⇣ ˜ j a j a µ = µ = µ , ` ` µ ⌘ a 1 ··· a s − 1 ⌘ a 1 ··· a s − 1 ! + e ! − e ⇣ ⇣ ˜ t a 1 ··· a s − 1 t a 1 ··· a s − 1 = = , µ µ ` ` µ µ 7

Introduction and overview of higher-spin theories in three dimensions • The asymptotic symmetry algebra for theories with higher spin in AdS 3 have been examined in [ M. Henneaux, S. J. Rey arXiv:1008.4579 ] and [ A. Campoleoni, S. Fredenhagen, S. Pfenninger, S. Theisen arXiv:1008.4744 ]. They found that a Brown-Henneaux like analysis for a theory with maximal spin N in the bulk yields a asymptotic W N symmetry algebra. 8