Flat Space Holography
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1 Flat Space Holography Daniel Grumiller Institute for Theoretical Physics TU Wien Quantum vacuum and gravitation Mainz, June 2015 based on work w. Afshar, Bagchi, Basu, Detournay, Fareghbal, Gary, Riegler, Rosseel, Salzer, Sarkar, Schöller, Simon,...
2 Some of our papers on flat space holography A. Bagchi, R. Basu, D. Grumiller and M. Riegler, Entanglement entropy in Galilean conformal field theories and flat holography, Phys. Rev. Lett. 114 (2015) 11, [arxiv: ]. H. Afshar, A. Bagchi, R. Fareghbal, D. Grumiller and J. Rosseel, Spin-3 Gravity in Three-Dimensional Flat Space, Phys. Rev. Lett. 111 (2013) 12, [arxiv: ]. A. Bagchi, S. Detournay, D. Grumiller and J. Simon, Cosmic Evolution from Phase Transition of Three-Dimensional Flat Space, Phys. Rev. Lett. 111 (2013) 18, [arxiv: ]. A. Bagchi, S. Detournay and D. Grumiller, Flat-Space Chiral Gravity, Phys. Rev. Lett. 109 (2012) [arxiv: ]. S. Detournay, D. Grumiller, F. Schöller and J. Simon, Variational principle and 1-point functions in 3-dimensional flat space Einstein gravity, Phys. Rev. D 89 (2014) 8, [arxiv: ]. Thanks Daniel Grumiller to Bob McNees Flatfor Space providing Holography the LATEX beamerclass! 2/17
3 Outline Motivations Holography basics Flat space holography Daniel Grumiller Flat Space Holography 3/17
4 Outline Motivations Holography basics Flat space holography Daniel Grumiller Flat Space Holography Motivations 4/17
5 Quote from the webpage of this workshop The aim of the program is to analyze from a modern perspective QFT methods, like renormalization group and conformal anomalies, and their applications in astrophysics and cosmology with special focus on black hole physics and the study of analogue systems. This talk focuses on holography. Daniel Grumiller Flat Space Holography Motivations 5/17
6 Quote from the webpage of this workshop The aim of the program is to analyze from a modern perspective QFT methods, like renormalization group and conformal anomalies, and their applications in astrophysics and cosmology with special focus on black hole physics and the study of analogue systems. This talk focuses on holography. QFT quantum gravity Daniel Grumiller Flat Space Holography Motivations 5/17
7 Quote from the webpage of this workshop The aim of the program is to analyze from a modern perspective QFT methods, like renormalization group and conformal anomalies, and their applications in astrophysics and cosmology with special focus on black hole physics and the study of analogue systems. This talk focuses on holography. QFT quantum gravity RG flow holographic RG flow Daniel Grumiller Flat Space Holography Motivations 5/17
8 Quote from the webpage of this workshop The aim of the program is to analyze from a modern perspective QFT methods, like renormalization group and conformal anomalies, and their applications in astrophysics and cosmology with special focus on black hole physics and the study of analogue systems. This talk focuses on holography. QFT quantum gravity RG flow holographic RG flow conformal anomalies properties of gravity action Daniel Grumiller Flat Space Holography Motivations 5/17
9 Quote from the webpage of this workshop The aim of the program is to analyze from a modern perspective QFT methods, like renormalization group and conformal anomalies, and their applications in astrophysics and cosmology with special focus on black hole physics and the study of analogue systems. This talk focuses on holography. QFT quantum gravity RG flow holographic RG flow conformal anomalies properties of gravity action thermal states in CFT black holes in AdS Daniel Grumiller Flat Space Holography Motivations 5/17
10 Quote from the webpage of this workshop The aim of the program is to analyze from a modern perspective QFT methods, like renormalization group and conformal anomalies, and their applications in astrophysics and cosmology with special focus on black hole physics and the study of analogue systems. This talk focuses on holography. QFT quantum gravity RG flow holographic RG flow conformal anomalies properties of gravity action thermal states in CFT black holes in AdS applications of holography Daniel Grumiller Flat Space Holography Motivations 5/17
11 Quote from the webpage of this workshop The aim of the program is to analyze from a modern perspective QFT methods, like renormalization group and conformal anomalies, and their applications in astrophysics and cosmology with special focus on black hole physics and the study of analogue systems. This talk focuses on holography. QFT quantum gravity RG flow holographic RG flow conformal anomalies properties of gravity action thermal states in CFT black holes in AdS applications of holography generalize holography beyond AdS/CFT? Daniel Grumiller Flat Space Holography Motivations 5/17
12 Quote from the webpage of this workshop The aim of the program is to analyze from a modern perspective QFT methods, like renormalization group and conformal anomalies, and their applications in astrophysics and cosmology with special focus on black hole physics and the study of analogue systems. This talk focuses on holography. QFT quantum gravity RG flow holographic RG flow conformal anomalies properties of gravity action thermal states in CFT black holes in AdS applications of holography generalize holography beyond AdS/CFT? Main question: how general is holography? Daniel Grumiller Flat Space Holography Motivations 5/17
13 Testing the holographic principle How general is holography? Daniel Grumiller Flat Space Holography Motivations 6/17
14 Testing the holographic principle How general is holography? To what extent do (previous) lessons rely on the particular constructions used to date? Are they tied to stringy effects and to string theory in particular, or are they general lessons for quantum gravity? see numerous talks at KITP workshop Bits, Branes, Black Holes 2012 and at ESI workshop Higher Spin Gravity 2012 Daniel Grumiller Flat Space Holography Motivations 6/17
15 Testing the holographic principle How general is holography? To what extent do (previous) lessons rely on the particular constructions used to date? Are they tied to stringy effects and to string theory in particular, or are they general lessons for quantum gravity? Does holography apply only to unitary theories? originally holography motivated by unitarity Daniel Grumiller Flat Space Holography Motivations 6/17
16 Testing the holographic principle How general is holography? To what extent do (previous) lessons rely on the particular constructions used to date? Are they tied to stringy effects and to string theory in particular, or are they general lessons for quantum gravity? Does holography apply only to unitary theories? originally holography motivated by unitarity plausible AdS/CFT-like correspondence could work non-unitarily AdS/log CFT first example of non-unitary holography DG, (Jackiw), Johansson 08; Skenderis, Taylor, van Rees 09; Henneaux, Martinez, Troncoso 09; Maloney, Song, Strominger 09; DG, Sachs/Hohm 09; Gaberdiel, DG, Vassilevich 10;... DG, Riedler, Rosseel, Zojer 13 recent proposal by Vafa 14 Daniel Grumiller Flat Space Holography Motivations 6/17
17 Testing the holographic principle How general is holography? To what extent do (previous) lessons rely on the particular constructions used to date? Are they tied to stringy effects and to string theory in particular, or are they general lessons for quantum gravity? Does holography apply only to unitary theories? Can we establish a flat space holographic dictionary? the answer appears to be yes see my current talk and recent papers by Bagchi et al., Barnich et al., Strominger et al., Daniel Grumiller Flat Space Holography Motivations 6/17
18 Testing the holographic principle How general is holography? To what extent do (previous) lessons rely on the particular constructions used to date? Are they tied to stringy effects and to string theory in particular, or are they general lessons for quantum gravity? Does holography apply only to unitary theories? Can we establish a flat space holographic dictionary? Generic non-ads holography/higher spin holography? non-trivial hints that it might work at least in 2+1 dimensions Gary, DG Rashkov 12; Afshar et al 12; Gutperle et al 14-15; Gary, DG, Prohazka, Rey 14;... Daniel Grumiller Flat Space Holography Motivations 6/17
19 Testing the holographic principle How general is holography? To what extent do (previous) lessons rely on the particular constructions used to date? Are they tied to stringy effects and to string theory in particular, or are they general lessons for quantum gravity? Does holography apply only to unitary theories? Can we establish a flat space holographic dictionary? Generic non-ads holography/higher spin holography? Address questions above in simple class of 3D toy models Exploit gauge theoretic Chern Simons formulation Restrict to kinematic questions, like (asymptotic) symmetries Daniel Grumiller Flat Space Holography Motivations 6/17
20 Goals of this talk 1. Review general aspects of holography in 3D Daniel Grumiller Flat Space Holography Motivations 7/17
21 Goals of this talk 1. Review general aspects of holography in 3D 2. Discuss flat space holography Daniel Grumiller Flat Space Holography Motivations 7/17
22 Goals of this talk 1. Review general aspects of holography in 3D 2. Discuss flat space holography 3. List selected open issues Daniel Grumiller Flat Space Holography Motivations 7/17
23 Goals of this talk 1. Review general aspects of holography in 3D 2. Discuss flat space holography 3. List selected open issues Address these issues in 3D! Daniel Grumiller Flat Space Holography Motivations 7/17
24 Outline Motivations Holography basics Flat space holography Daniel Grumiller Flat Space Holography Holography basics 8/17
25 Assumptions Working assumptions: 3D Daniel Grumiller Flat Space Holography Holography basics 9/17
26 Assumptions Working assumptions: 3D Restrict to pure gravity theories Daniel Grumiller Flat Space Holography Holography basics 9/17
27 Assumptions Working assumptions: 3D Restrict to pure gravity theories Define quantum gravity by its dual field theory Interesting dichotomy: Either dual field theory exists useful toy model for quantum gravity Or gravitational theory needs UV completion (within string theory) indication of inevitability of string theory Daniel Grumiller Flat Space Holography Holography basics 9/17
28 Assumptions Working assumptions: 3D Restrict to pure gravity theories Define quantum gravity by its dual field theory Interesting dichotomy: Either dual field theory exists useful toy model for quantum gravity Or gravitational theory needs UV completion (within string theory) indication of inevitability of string theory This talk: Remain agnostic about dichotomy Focus on generic features of dual field theories that do not require string theory embedding Daniel Grumiller Flat Space Holography Holography basics 9/17
29 Gravity in 3D AdS 3 gravity Lowest dimension with black holes and (off-shell) gravitons Daniel Grumiller Flat Space Holography Holography basics 10/17
30 Gravity in 3D AdS 3 gravity Lowest dimension with black holes and (off-shell) gravitons Weyl = 0, thus Riemann = Ricci Daniel Grumiller Flat Space Holography Holography basics 10/17
31 Gravity in 3D AdS 3 gravity Lowest dimension with black holes and (off-shell) gravitons Weyl = 0, thus Riemann = Ricci Einstein gravity: no on-shell gravitons Daniel Grumiller Flat Space Holography Holography basics 10/17
32 Gravity in 3D AdS 3 gravity Lowest dimension with black holes and (off-shell) gravitons Weyl = 0, thus Riemann = Ricci Einstein gravity: no on-shell gravitons Formulation as topological gauge theory (Chern Simons) Daniel Grumiller Flat Space Holography Holography basics 10/17
33 Gravity in 3D AdS 3 gravity Lowest dimension with black holes and (off-shell) gravitons Weyl = 0, thus Riemann = Ricci Einstein gravity: no on-shell gravitons Formulation as topological gauge theory (Chern Simons) Dual field theory (if it exists): 2D Interesting generic constraints from CFT 2! e.g. Hellerman 09, Hartman, Keller, Stoica 14 Daniel Grumiller Flat Space Holography Holography basics 10/17
34 Gravity in 3D AdS 3 gravity Lowest dimension with black holes and (off-shell) gravitons Weyl = 0, thus Riemann = Ricci Einstein gravity: no on-shell gravitons Formulation as topological gauge theory (Chern Simons) Dual field theory (if it exists): 2D Infinite dimensional asymptotic symmetries (Brown Henneaux) Daniel Grumiller Flat Space Holography Holography basics 10/17
35 Gravity in 3D AdS 3 gravity Lowest dimension with black holes and (off-shell) gravitons Weyl = 0, thus Riemann = Ricci Einstein gravity: no on-shell gravitons Formulation as topological gauge theory (Chern Simons) Dual field theory (if it exists): 2D Infinite dimensional asymptotic symmetries (Brown Henneaux) Black holes as orbifolds of AdS 3 (BTZ) Daniel Grumiller Flat Space Holography Holography basics 10/17
36 Gravity in 3D AdS 3 gravity Lowest dimension with black holes and (off-shell) gravitons Weyl = 0, thus Riemann = Ricci Einstein gravity: no on-shell gravitons Formulation as topological gauge theory (Chern Simons) Dual field theory (if it exists): 2D Infinite dimensional asymptotic symmetries (Brown Henneaux) Black holes as orbifolds of AdS 3 (BTZ) Simple microstate counting from AdS 3 /CFT 2 Daniel Grumiller Flat Space Holography Holography basics 10/17
37 Gravity in 3D AdS 3 gravity Lowest dimension with black holes and (off-shell) gravitons Weyl = 0, thus Riemann = Ricci Einstein gravity: no on-shell gravitons Formulation as topological gauge theory (Chern Simons) Dual field theory (if it exists): 2D Infinite dimensional asymptotic symmetries (Brown Henneaux) Black holes as orbifolds of AdS 3 (BTZ) Simple microstate counting from AdS 3 /CFT 2 Hawking Page phase transition hot AdS BTZ Daniel Grumiller Flat Space Holography Holography basics 10/17
38 Gravity in 3D AdS 3 gravity Lowest dimension with black holes and (off-shell) gravitons Weyl = 0, thus Riemann = Ricci Einstein gravity: no on-shell gravitons Formulation as topological gauge theory (Chern Simons) Dual field theory (if it exists): 2D Infinite dimensional asymptotic symmetries (Brown Henneaux) Black holes as orbifolds of AdS 3 (BTZ) Simple microstate counting from AdS 3 /CFT 2 Hawking Page phase transition hot AdS BTZ Simple checks of Ryu Takayanagi proposal Daniel Grumiller Flat Space Holography Holography basics 10/17
39 Gravity in 3D AdS 3 gravity Lowest dimension with black holes and (off-shell) gravitons Weyl = 0, thus Riemann = Ricci Einstein gravity: no on-shell gravitons Formulation as topological gauge theory (Chern Simons) Dual field theory (if it exists): 2D Infinite dimensional asymptotic symmetries (Brown Henneaux) Black holes as orbifolds of AdS 3 (BTZ) Simple microstate counting from AdS 3 /CFT 2 Hawking Page phase transition hot AdS BTZ Simple checks of Ryu Takayanagi proposal Caveat: while there are many string compactifications with AdS 3 factor, applying holography just to AdS 3 factor does not capture everything! Daniel Grumiller Flat Space Holography Holography basics 10/17
40 Picturesque analogy: soap films Both soap films and Chern Simons theories have essentially no bulk dynamics highly non-trivial boundary dynamics most of the physics determined by boundary conditions esthetic appeal (at least for me) Daniel Grumiller Flat Space Holography Holography basics 11/17
41 Outline Motivations Holography basics Flat space holography Daniel Grumiller Flat Space Holography Flat space holography 12/17
42 Flat space holography (Barnich et al, Bagchi et al, Strominger et al,...) if holography is true must work in flat space Just take large AdS radius limit of 10 4 AdS/CFT papers? Daniel Grumiller Flat Space Holography Flat space holography 13/17
43 Flat space holography (Barnich et al, Bagchi et al, Strominger et al,...) if holography is true must work in flat space Just take large AdS radius limit of 10 4 AdS/CFT papers? Works straightforwardly sometimes, otherwise not Daniel Grumiller Flat Space Holography Flat space holography 13/17
44 Flat space holography (Barnich et al, Bagchi et al, Strominger et al,...) if holography is true must work in flat space Just take large AdS radius limit of 10 4 AdS/CFT papers? Works straightforwardly sometimes, otherwise not Example where it works nicely: asymptotic symmetry algebra Daniel Grumiller Flat Space Holography Flat space holography 13/17
45 Flat space holography (Barnich et al, Bagchi et al, Strominger et al,...) if holography is true must work in flat space Just take large AdS radius limit of 10 4 AdS/CFT papers? Works straightforwardly sometimes, otherwise not Example where it works nicely: asymptotic symmetry algebra Take linear combinations of Virasoro generators L n, Ln L n = L n L n M n = 1 ( Ln + l L ) n Daniel Grumiller Flat Space Holography Flat space holography 13/17
46 Flat space holography (Barnich et al, Bagchi et al, Strominger et al,...) if holography is true must work in flat space Just take large AdS radius limit of 10 4 AdS/CFT papers? Works straightforwardly sometimes, otherwise not Example where it works nicely: asymptotic symmetry algebra Take linear combinations of Virasoro generators L n, Ln L n = L n L n M n = 1 ( Ln + l L ) n Make Inönü Wigner contraction l on ASA [L n, L m] = (n m) L n+m + cl 12 (n3 n) δ n+m, 0 [L n, M m] = (n m) M n+m + cm 12 (n3 n) δ n+m, 0 [M n, M m] = 0 Daniel Grumiller Flat Space Holography Flat space holography 13/17
47 Flat space holography (Barnich et al, Bagchi et al, Strominger et al,...) if holography is true must work in flat space Just take large AdS radius limit of 10 4 AdS/CFT papers? Works straightforwardly sometimes, otherwise not Example where it works nicely: asymptotic symmetry algebra Take linear combinations of Virasoro generators L n, Ln L n = L n L n M n = 1 ( Ln + l L ) n Make Inönü Wigner contraction l on ASA [L n, L m] = (n m) L n+m + cl 12 (n3 n) δ n+m, 0 [L n, M m] = (n m) M n+m + cm 12 (n3 n) δ n+m, 0 [M n, M m] = 0 This is nothing but the BMS 3 algebra (or GCA 2, URCA 2, CCA 2 )! Daniel Grumiller Flat Space Holography Flat space holography 13/17
48 Flat space holography (Barnich et al, Bagchi et al, Strominger et al,...) if holography is true must work in flat space Just take large AdS radius limit of 10 4 AdS/CFT papers? Works straightforwardly sometimes, otherwise not Example where it works nicely: asymptotic symmetry algebra Take linear combinations of Virasoro generators L n, Ln L n = L n L n M n = 1 ( Ln + l L ) n Make Inönü Wigner contraction l on ASA [L n, L m] = (n m) L n+m + cl 12 (n3 n) δ n+m, 0 [L n, M m] = (n m) M n+m + cm 12 (n3 n) δ n+m, 0 [M n, M m] = 0 This is nothing but the BMS 3 algebra (or GCA 2, URCA 2, CCA 2 )! Example where it does not work easily: boundary conditions Daniel Grumiller Flat Space Holography Flat space holography 13/17
49 Flat space holography (Barnich et al, Bagchi et al, Strominger et al,...) if holography is true must work in flat space Just take large AdS radius limit of 10 4 AdS/CFT papers? Works straightforwardly sometimes, otherwise not Example where it works nicely: asymptotic symmetry algebra Take linear combinations of Virasoro generators L n, Ln L n = L n L n M n = 1 ( Ln + l L ) n Make Inönü Wigner contraction l on ASA [L n, L m] = (n m) L n+m + cl 12 (n3 n) δ n+m, 0 [L n, M m] = (n m) M n+m + cm 12 (n3 n) δ n+m, 0 [M n, M m] = 0 This is nothing but the BMS 3 algebra (or GCA 2, URCA 2, CCA 2 )! Example where it does not work easily: boundary conditions Example where it does not work: highest weight conditions Daniel Grumiller Flat Space Holography Flat space holography 13/17
50 Flat space Einstein gravity as isl(2) Chern Simons theory Daniel Grumiller Flat Space Holography Flat space holography 14/17
51 Flat space Einstein gravity as isl(2) Chern Simons theory AdS gravity in CS formulation: sl(2) sl(2) gauge algebra Daniel Grumiller Flat Space Holography Flat space holography 14/17
52 Flat space Einstein gravity as isl(2) Chern Simons theory AdS gravity in CS formulation: sl(2) sl(2) gauge algebra Flat space: isl(2) gauge algebra S flat CS = k A da + 2 4π 3 A A A with isl(2) connection (a = 0, ±1) A = e a M a + ω a L a isl(2) algebra (global part of BMS/GCA algebra) [L a, L b ] = (a b)l a+b [L a, M b ] = (a b)m a+b [M a, M b ] = 0 Note: e a dreibein, ω a (dualized) spin-connection Bulk EOM: gauge flatness F = da + A A = 0 Daniel Grumiller Flat Space Holography Flat space holography 14/17
53 Flat space Einstein gravity as isl(2) Chern Simons theory AdS gravity in CS formulation: sl(2) sl(2) gauge algebra Flat space: isl(2) gauge algebra S flat CS = k A da + 2 4π 3 A A A with isl(2) connection (a = 0, ±1) A = e a M a + ω a L a Boundary conditions in CS formulation: A(r, u, ϕ) = b 1 (r) ( d+a(u, ϕ) + o(1) ) b(r) Daniel Grumiller Flat Space Holography Flat space holography 14/17
54 Flat space Einstein gravity as isl(2) Chern Simons theory AdS gravity in CS formulation: sl(2) sl(2) gauge algebra Flat space: isl(2) gauge algebra S flat CS = k A da + 2 4π 3 A A A with isl(2) connection (a = 0, ±1) A = e a M a + ω a L a Boundary conditions in CS formulation: A(r, u, ϕ) = b 1 (r) ( d+a(u, ϕ) + o(1) ) b(r) Flat space boundary conditions: b(r) = exp ( 1 2 rm 1) and a(u, ϕ) = ( M 1 M(ϕ)M 1 ) du + ( L1 M(ϕ)L 1 N(u, ϕ)m 1 ) dϕ with N(u, ϕ) = L(ϕ) + u 2 M (ϕ) Daniel Grumiller Flat Space Holography Flat space holography 14/17
55 Flat space Einstein gravity as isl(2) Chern Simons theory AdS gravity in CS formulation: sl(2) sl(2) gauge algebra Flat space: isl(2) gauge algebra S flat CS = k A da + 2 4π 3 A A A with isl(2) connection (a = 0, ±1) A = e a M a + ω a L a Boundary conditions in CS formulation: A(r, u, ϕ) = b 1 (r) ( d+a(u, ϕ) + o(1) ) b(r) Flat space boundary conditions: b(r) = exp ( 1 2 rm 1) and a(u, ϕ) = ( M 1 M(ϕ)M 1 ) du + ( L1 M(ϕ)L 1 N(u, ϕ)m 1 ) dϕ with N(u, ϕ) = L(ϕ) + u 2 M (ϕ) metric g µν 1 2 tr A µ A ν ds 2 = M du 2 2 du dr+2n du dϕ+r 2 dϕ 2 Daniel Grumiller Flat Space Holography Flat space holography 14/17
56 Selected recent results Classical saddle points of flat space Einstein gravity: ds 2 = M du 2 2 du dr + 2N du dϕ + r 2 dϕ 2 Minkowski: M = 1, N = 0 Flat-space cosmologies (FSC): M > 0, N 0 (analogue of BTZ) Note: different way to write FSC: ds 2 = dτ 2 + (Eτ)2 dx (Eτ) 2 + ( 1 + (Eτ) 2) ( dy + (Eτ)2 1 + (Eτ) 2 dx) 2 Time-dependent background (Cornalba, Costa 02) Penrose diagram: like Schwarzschild turned by 90 degrees Obtained as limit from region between inner/outer BTZ horizons (Barnich, Gomberoff, Gonzalez 12) Daniel Grumiller Flat Space Holography Flat space holography 15/17
57 Selected recent results Classical saddle points of flat space Einstein gravity: ds 2 = M du 2 2 du dr + 2N du dϕ + r 2 dϕ 2 Dual field theory? Daniel Grumiller Flat Space Holography Flat space holography 15/17
58 Selected recent results Classical saddle points of flat space Einstein gravity: Dual field theory? ds 2 = M du 2 2 du dr + 2N du dϕ + r 2 dϕ 2 Galilean conformal field theory! (Bagchi et al, Barnich et al) Algebra: [L n, L m ] = (n m)l n+m + c L 12 δ n+m, 0 [L n, M m ] = (n m)m n+m + c M 12 δ n+m, 0 [M n, M m ] = 0 M n : supertranslations, L n : superrotations Gravity interpretation: ultra-relativistic boost (AdS bdry maps to scri) Daniel Grumiller Flat Space Holography Flat space holography 15/17
59 Selected recent results Classical saddle points of flat space Einstein gravity: ds 2 = M du 2 2 du dr + 2N du dϕ + r 2 dϕ 2 Dual field theory? Microstate counting? Daniel Grumiller Flat Space Holography Flat space holography 15/17
60 Selected recent results Classical saddle points of flat space Einstein gravity: Dual field theory? Microstate counting? ds 2 = M du 2 2 du dr + 2N du dϕ + r 2 dϕ 2 Works! (Bagchi, Detournay, Fareghbal, Simon 13, Barnich 13) S gravity = S BH = Area cm = 2πh L = S GCFT 4G N 2h M Also works as limit from Cardy formula (Riegler 14, Fareghbal, Naseh 14) Daniel Grumiller Flat Space Holography Flat space holography 15/17
61 Selected recent results Classical saddle points of flat space Einstein gravity: ds 2 = M du 2 2 du dr + 2N du dϕ + r 2 dϕ 2 Dual field theory? Microstate counting? Phase transition between flat space and FSC? Daniel Grumiller Flat Space Holography Flat space holography 15/17
62 Selected recent results Classical saddle points of flat space Einstein gravity: Dual field theory? Microstate counting? ds 2 = M du 2 2 du dr + 2N du dϕ + r 2 dϕ 2 Phase transition between flat space and FSC? Exists! (Bagchi, Detournay, DG, Simon 13) Small temperatures: flat space thermodynamically stable Large temperatures: FSC thermodynamically stable Daniel Grumiller Flat Space Holography Flat space holography 15/17
63 Selected recent results Classical saddle points of flat space Einstein gravity: Dual field theory? Microstate counting? ds 2 = M du 2 2 du dr + 2N du dϕ + r 2 dϕ 2 Phase transition between flat space and FSC? Holographic renormalization, variational principle, vev/source structure? Daniel Grumiller Flat Space Holography Flat space holography 15/17
64 Selected recent results Classical saddle points of flat space Einstein gravity: Dual field theory? Microstate counting? ds 2 = M du 2 2 du dr + 2N du dϕ + r 2 dϕ 2 Phase transition between flat space and FSC? Holographic renormalization, variational principle, vev/source structure? Works! (Detournay, DG, Schöller, Simon 14) Interesting technical detail: boundary term half of GHY Γ = 1 d 3 x 1 g R d 2 x γ K 16πG N 16πG N δγ = 0 for all metric variations that preserve flat space bc s Daniel Grumiller Flat Space Holography Flat space holography 15/17
65 Selected recent results Classical saddle points of flat space Einstein gravity: Dual field theory? Microstate counting? ds 2 = M du 2 2 du dr + 2N du dϕ + r 2 dϕ 2 Phase transition between flat space and FSC? Holographic renormalization, variational principle, vev/source structure? (Holographic) entanglement entropy? Daniel Grumiller Flat Space Holography Flat space holography 15/17
66 Selected recent results Classical saddle points of flat space Einstein gravity: ds 2 = M du 2 2 du dr + 2N du dϕ + r 2 dϕ 2 Dual field theory? Microstate counting? Phase transition between flat space and FSC? Holographic renormalization, variational principle, vev/source structure? (Holographic) entanglement entropy? Works! (Bagchi, Basu, DG, Riegler 14) S GCFT EE = c L 6 ln l x + }{{ a} like CFT l y l x c M 6 }{{} like grav anomaly Calculation on gravity side confirms result above (using Wilson lines in CS formulation) Daniel Grumiller Flat Space Holography Flat space holography 15/17
67 Generalizations & open issues Recent generalizations: adding chemical potentials Works! (Gary, DG, Riegler, Rosseel 14) In CS formulation: A 0 A 0 + µ Daniel Grumiller Flat Space Holography Flat space holography 16/17
68 Generalizations & open issues Recent generalizations: adding chemical potentials 3-derivative theory: flat space chiral gravity (Bagchi, Detournay, DG 12) Conformal CS gravity at level k = 1 with flat space boundary conditions conjectured to be dual to chiral half of monster CFT. Action (gravity side): I CSG = k 4π d 3 x g ε λµν Γ ρ λσ( µ Γ σ νρ Γσ µτ Γ τ ) νρ Partition function (field theory side, see Witten 07): Z(q) = J(q) = 1 q q + O(q2 ) Note: ln = 4π+quantum corrections Daniel Grumiller Flat Space Holography Flat space holography 16/17
69 Generalizations & open issues Recent generalizations: adding chemical potentials 3-derivative theory: flat space chiral gravity (Bagchi, Detournay, DG 12) generalization to supergravity Works! (Barnich, Donnay, Matulich, Troncoso 14) Asymptotic symmetry algebra = super-bms 3 Daniel Grumiller Flat Space Holography Flat space holography 16/17
70 Generalizations & open issues Recent generalizations: adding chemical potentials 3-derivative theory: flat space chiral gravity (Bagchi, Detournay, DG 12) generalization to supergravity flat space higher spin gravity Remarkably it exists! (Afshar, Bagchi, Fareghbal, DG, Rosseel 13; Gonzalez, Matulich, Pino, Troncoso 13) New type of algebra: W-like BMS ( BMW ) [U n, U m] = (n m)(2n 2 + 2m 2 nm 8)L n+m (n m)λ n+m c M 96( ) c L (n m)θ n+m + cl 12 n(n2 1)(n 2 4) δ n+m, 0 c 2 M [U n, V m] = (n m)(2n 2 + 2m 2 nm 8)M n+m + 96 c M (n m)θ n+m + cm 12 n(n2 1)(n 2 4) δ n+m, 0 [L, L], [L, M],[M, M] as in BMS 3 [L, U], [L, V ], [M, U], [M, V ] as in isl(3) Daniel Grumiller Flat Space Holography Flat space holography 16/17
71 Generalizations & open issues Recent generalizations: adding chemical potentials 3-derivative theory: flat space chiral gravity (Bagchi, Detournay, DG 12) generalization to supergravity flat space higher spin gravity Some open issues: Further checks in 3D (n-point correlators, partition function,...) Daniel Grumiller Flat Space Holography Flat space holography 16/17
72 Generalizations & open issues Recent generalizations: adding chemical potentials 3-derivative theory: flat space chiral gravity (Bagchi, Detournay, DG 12) generalization to supergravity flat space higher spin gravity Some open issues: Further checks in 3D (n-point correlators, partition function,...) Further generalizations in 3D (massive gravity, adding matter,...) Daniel Grumiller Flat Space Holography Flat space holography 16/17
73 Generalizations & open issues Recent generalizations: adding chemical potentials 3-derivative theory: flat space chiral gravity (Bagchi, Detournay, DG 12) generalization to supergravity flat space higher spin gravity Some open issues: Further checks in 3D (n-point correlators, partition function,...) Further generalizations in 3D (massive gravity, adding matter,...) Generalization to 4D? (Barnich et al, Strominger et al) Daniel Grumiller Flat Space Holography Flat space holography 16/17
74 Generalizations & open issues Recent generalizations: adding chemical potentials 3-derivative theory: flat space chiral gravity (Bagchi, Detournay, DG 12) generalization to supergravity flat space higher spin gravity Some open issues: Further checks in 3D (n-point correlators, partition function,...) Further generalizations in 3D (massive gravity, adding matter,...) Generalization to 4D? (Barnich et al, Strominger et al) Flat space limit of usual AdS 5 /CFT 4 correspondence? Daniel Grumiller Flat Space Holography Flat space holography 16/17
75 Generalizations & open issues Recent generalizations: adding chemical potentials 3-derivative theory: flat space chiral gravity (Bagchi, Detournay, DG 12) generalization to supergravity flat space higher spin gravity Some open issues: Further checks in 3D (n-point correlators, partition function,...) Further generalizations in 3D (massive gravity, adding matter,...) Generalization to 4D? (Barnich et al, Strominger et al) Flat space limit of usual AdS 5 /CFT 4 correspondence? holography seems to work in flat space Daniel Grumiller Flat Space Holography Flat space holography 16/17
76 Generalizations & open issues Recent generalizations: adding chemical potentials 3-derivative theory: flat space chiral gravity (Bagchi, Detournay, DG 12) generalization to supergravity flat space higher spin gravity Some open issues: Further checks in 3D (n-point correlators, partition function,...) Further generalizations in 3D (massive gravity, adding matter,...) Generalization to 4D? (Barnich et al, Strominger et al) Flat space limit of usual AdS 5 /CFT 4 correspondence? holography seems to work in flat space holography more general than AdS/CFT Daniel Grumiller Flat Space Holography Flat space holography 16/17
77 Generalizations & open issues Recent generalizations: adding chemical potentials 3-derivative theory: flat space chiral gravity (Bagchi, Detournay, DG 12) generalization to supergravity flat space higher spin gravity Some open issues: Further checks in 3D (n-point correlators, partition function,...) Further generalizations in 3D (massive gravity, adding matter,...) Generalization to 4D? (Barnich et al, Strominger et al) Flat space limit of usual AdS 5 /CFT 4 correspondence? holography seems to work in flat space holography more general than AdS/CFT (when) does it work even more generally? Daniel Grumiller Flat Space Holography Flat space holography 16/17
78 Thanks for your attention! Vladimir Bulatov, M.C.Escher Circle Limit III in a rectangle Daniel Grumiller Flat Space Holography Flat space holography 17/17
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