Massive type IIA string theory cannot be strongly coupled Daniel L. Jafferis Institute for Advanced Study 16 November, 2010 Rutgers University Based on.

Slides:



Advertisements
Similar presentations
Can Integrable Cosmologies fit into Gauged Supergravity? Can Integrable Cosmologies fit into Gauged Supergravity? Pietro Frè University of Torino & Embassy.
Advertisements

Theories of gravity in 5D brane-world scenarios
Analysis of QCD via Supergravity S. Sugimoto (YITP) based on hep-th/ (T. Ibaraki + S.S.) Windows to new paradigm in particle Sendai.
Toward M5-branes from ABJM action Based on going project with Seiji Terashima (YITP, Kyoto U. ) Futoshi Yagi (YITP, Kyoto U.)
On d=3 Yang-Mills-Chern- Simons theories with “fractional branes” and their gravity duals Ofer Aharony Weizmann Institute of Science 14 th Itzykson Meeting.
Spectroscopy of fermionic operators in AdS/CFT with flavor Ingo Kirsch Workshop „QCD and String Theory“ Ringberg Castle, Tegernsee, July 2-8, 2006 I. K.,
Brane-World Inflation
Summing planar diagrams
Non-perturbative effects in string theory compactifications Sergey Alexandrov Laboratoire Charles Coulomb Université Montpellier 2 in collaboration with.
A journey inside planar pure QED CP3 lunch meeting By Bruno Bertrand November 19 th 2004.
Heterotic strings and fluxes Based on: K. Becker, S. Sethi, Torsional heterotic geometries, to appear. K. Becker, C. Bertinato, Y-C. Chung, G. Guo, Supersymmetry.
Hep-ph/ , with M. Carena (FNAL), E. Pontón (Columbia) and C. Wagner (ANL) New Ideas in Randall-Sundrum Models José Santiago Theory Group (FNAL)
BRANE SOLUTIONS AND RG FLOW UNIVERSIDADE FEDERAL DE CAMPINA GRANDE September 2006 FRANCISCO A. BRITO.
Gauge/Gravity Duality 2 Prof Nick Evans AdS/CFT Correspondence TODAY Quarks Deforming AdS Confinement Chiral Symmetry Breaking LATER Other brane games.
Giant Magnon and Spike Solutions in String Theories Bum-Hoon Lee Center for Quantum SpaceTime(CQUeST)/Physics Dept. Sogang University, Seoul, Korea PAQFT08,
Chanyong Park 35 th Johns Hopkins Workshop ( Budapest, June 2011 ) Based on Phys. Rev. D 83, (2011) arXiv : arXiv :
Extremal Single-charge Small Black holes Aninda Sinha DAMTP, Cambridge University, UK hep-th/ (to appear in CQG) with Nemani Suryanarayana(Perimeter),
The superconformal index for N=6 Chern-Simons theory Seok Kim (Imperial College London) talk based on: arXiv: closely related works: J. Bhattacharya.
Gauge/Gravity Duality 2 Prof Nick Evans AdS/CFT Correspondence TODAY Quarks Deforming AdS Confinement Chiral Symmetry Breaking LATER Other brane games.
Supersymmetry and Gauge Symmetry Breaking from Intersecting Branes A. Giveon, D.K. hep-th/
The effective action on the confining string Ofer Aharony Weizmann Institute of Science 5 th Crete Regional Meeting in String Theory, Kolymbari, June 30,
QCD – from the vacuum to high temperature an analytical approach an analytical approach.
Dual gravity approach to near-equilibrium processes in strongly coupled gauge theories Andrei Starinets Hadrons and Strings Trento July 20, 2006 Perimeter.
Planar diagrams in light-cone gauge hep-th/ M. Kruczenski Purdue University Based on:
3-Sasakian geometry from M2 branes Daniel L. Jafferis Rutgers University Kähler and Sasakian Geometry in Rome 19 June, 2009 Based on work with: A. Tomasiello;
Electric-Magnetic Duality On A Half-Space Edward Witten Rutgers University May 12, 2008.
Takayuki Nagashima Tokyo Institute of Technology In collaboration with M.Eto (Pisa U.), T.Fujimori (TIT), M.Nitta (Keio U.), K.Ohashi (Cambridge U.) and.
AGT 関係式 (1) Gaiotto の議論 (String Advanced Lectures No.18) 高エネルギー加速器研究機構 (KEK) 素粒子原子核研究所 (IPNS) 柴 正太郎 2010 年 6 月 2 日(水) 12:30-14:30.
ADE Matrix Models in Four Dimensional QFT DK, J. Lin arXiv: , ``Strings, Matrices, Integrability’’ Paris, August 19, 2014.
Holographic Description of Quantum Black Hole on a Computer Yoshifumi Hyakutake (Ibaraki Univ.) Collaboration with M. Hanada ( YITP, Kyoto ), G. Ishiki.
The Squashed, Stretched and Warped Gets Perturbed The Squashed, Stretched and Warped Gets Perturbed Igor Klebanov PCTS and Department of Physics Talk at.
Exact Results for perturbative partition functions of theories with SU(2|4) symmetry Shinji Shimasaki (Kyoto University) JHEP1302, 148 (2013) (arXiv: [hep-th])
Multi-quark potential from AdS/QCD based on arXiv: Wen-Yu Wen Lattice QCD.
Finite N Index and Angular Momentum Bound from Gravity “KEK Theory Workshop 2007” Yu Nakayama, 13 th. Mar (University of Tokyo) Based on hep-th/
Matrix Cosmology Miao Li Institute of Theoretical Physics Chinese Academy of Science.
LLM geometries in M-theory and probe branes inside them Jun-Bao Wu IHEP, CAS Nov. 24, 2010, KITPC.
Anomalous U(1)΄s, Chern-Simons couplings and the Standard Model Pascal Anastasopoulos (INFN, Roma “Tor Vergata”) Pascal Anastasopoulos (INFN, Roma “Tor.
The effective action on the confining string Ofer Aharony Weizmann Institute of Science Based on: O.A. and Eyal Karzbrun, arXiv: O.A. and Zohar.
AGT 関係式 (2) AGT 関係式 (String Advanced Lectures No.19) 高エネルギー加速器研究機構 (KEK) 素粒子原子核研究所 (IPNS) 柴 正太郎 2010 年 6 月 9 日(水) 12:30-14:30.
InflationInflation Andrei Linde Lecture 2. Inflation as a theory of a harmonic oscillator Eternal Inflation.
Meta-stable Supersymmetry Breaking in an N=1 Perturbed Seiberg-Witten Theory Shin Sasaki (Univ. of Helsinki, Helsinki Inst. of Physics) Phys. Rev. D76.
2 Time Physics and Field theory
First Steps Towards a Theory of Quantum Gravity Mark Baumann Dec 6, 2006.
1 Superstring vertex operators in type IIB matrix model arXiv: [hep-th], [hep-th] Satoshi Nagaoka (KEK) with Yoshihisa Kitazawa (KEK &
Gauge/Gravity Duality Prof Nick Evans Big picture – slides Key computations - board TODAY Introduction Strings & Branes AdS/CFT Correspondence QCD-like.
Torsional heterotic geometries Katrin Becker ``14th Itzykson Meeting'' IPHT, Saclay, June 19, 2009.
On String Theory Duals of Lifshitz-like Fixed Point Tatsuo Azeyanagi (Kyoto University) Based on work arXiv: (to appear in JHEP) with Wei Li (IPMU)
The nonperturbative analyses for lower dimensional non-linear sigma models Etsuko Itou (Osaka University) 1.Introduction 2.The WRG equation for NLσM 3.Fixed.
Seiberg Duality James Barnard University of Durham.
Holographic Description of Quantum Black Hole on a Computer Yoshifumi Hyakutake (Ibaraki Univ.) Collaboration with M. Hanada ( YITP, Kyoto ), G. Ishiki.
B.-H.L, R. Nayak, K. Panigrahi, C. Park On the giant magnon and spike solutions for strings on AdS(3) x S**3. JHEP 0806:065,2008. arXiv: J. Kluson,
Exact Results for 5d SCFTs with gravity duals Daniel L. Jafferis Harvard University Yukawa International Seminar Kyoto, Japan Oct 15, 2012 D.J., Silviu.
P-Term Cosmology A.C. Davis (with C. Burrage) ,
Gauge/gravity duality in Einstein-dilaton theory Chanyong Park Workshop on String theory and cosmology (Pusan, ) Ref. S. Kulkarni,
ArXiv: (hep-th) Toshiaki Fujimori (Tokyo Institute of Technology) Minoru Eto, Sven Bjarke Gudnason, Kenichi Konishi, Muneto Nitta, Keisuke Ohashi.
1 Marginal Deformations and Penrose limits with continuous spectrum Toni Mateos Imperial College London Universitat de Barcelona, December 22, 2005.
Multiple Brane Dynamics: D-Branes to M-Branes Neil Lambert King’s College London Annual UK Theory Meeting Durham 18 December 2008 Up from String Theory.
“Applied” String Theory Pinaki Banerjee The Institute of Mathematical Sciences, Chennai Department of Physics, Visva Bharati 12 th July, 2013.
Can Integrable Cosmologies fit into Gauged Supergravity?
Dept.of Physics & Astrophysics
Quantum Mechanical Models for Near Extremal Black Holes
Counting the Microstates of a Kerr Black Hole
STRING THEORY AND M-THEORY: A Modern Introduction
dark matter Properties stable non-relativistic non-baryonic
Gravity from Entanglement and RG Flow
Heterotic strings and fluxes: status and prospects
Deformed Prepotential, Quantum Integrable System and Liouville Field Theory Kazunobu Maruyoshi  Yukawa Institute.
Hysteresis Curves from 11 dimensions
AGT 関係式(1) Gaiotto の議論 (String Advanced Lectures No.18)
String Theory: A Status Report Institute for Advanced Study
Presentation transcript:

Massive type IIA string theory cannot be strongly coupled Daniel L. Jafferis Institute for Advanced Study 16 November, 2010 Rutgers University Based on work with Aharony, Tomasiello, and Zaffaroni

Motivations What is the fate of massive IIA at strong coupling? What is the fate of massive IIA at strong coupling? What is the dual description of 3d CFTs at large N and fixed coupling? What is the dual description of 3d CFTs at large N and fixed coupling? Explore the N=1, 2 massive IIA AdS × CP 3 solutions and their dual CFTs. Explore the N=1, 2 massive IIA AdS × CP 3 solutions and their dual CFTs.

IIA string theory at strong coupling The strong coupling limit of IIA string theory is M-theory, so this regime is again described by supergravity. D0 branes have a mass 1/g s, and become light, producing the KK tower of the 11d theory. d s 2 11 = e ¡ 2 Á = 3 d s e 4 Á = 3 ( d x 11 + A ) 2

Massive IIA at strong coupling Would seem to be a lacuna in the web of string dualities. The D0 branes have tadpoles, There is no free “massive” parameter in 11d supergravity. A more fundamental question: are there any strongly coupled solutions of IIA supergravity? R F 0 A D 0

Behavior of 3d CFT at large N In the ‘t Hooft limit, one always finds a weakly coupled string dual. In 3d, it is natural to consider taking N large with k fixed. In the N=6 theory, this results in light disorder operators corresponding to the light D0 branes of IIA at strong coupling. There is an M-theory sugra description with entropy N 3/2. In the N=6 theory, this results in light disorder operators corresponding to the light D0 branes of IIA at strong coupling. There is an M-theory sugra description with entropy N 3/2. Is that the generic behavior? Is that the generic behavior? g s » ¸ = N i n A d S 5 an d g s » ¸ 5 = 4 = N i n A d S 4

A bound on the dilaton In string frame, the Einstein equations are this is exact up to 2 derivative order even when the coupling is large. The 00 component can be written using frame indices as where e ¡ 2 Á ¡ R MN + 2 r M r N Á ¡ 1 4 H M PQ H NPQ ¢ = P k = 0 ; 2 ; 4 T F k MN T F k MN = 1 2 ( k ¡ 1 ) ! F M M 2 ::: M k F NM 2 ::: M k ¡ 1 4 k! F M 1 ::: M k F M 1 ::: M k g MN 1 4 ( P k = 2 ; 4 F 2 0 ; k ¡ 1 + P k = 0 ; 2 ; 4 F 2 ? ; k ) F k = e 0 ^ F 0 ; k ¡ 1 + F ? ; k

Massive IIA solutions cannot be strongly coupled and weakly curved This equation is satisfied at every point in spacetime. All of the terms in parentheses on the left side must be small, otherwise the 2 derivative sugra action cannot be trusted. The fluxes, on a compact a-cycle are quantized. Thus is F 0 ≠ 0, then the rhs. Therefore. Typically, the lhs is order 1/R 2, thus ( ¿ ` ¡ 2 s ) Z C a e ¡ B X k F k = n a ( 2 ¼ ` s ) a ¡ 1 > 1 = ` 2 s e Á ¿ 1 e Á » < ` s = R.

In strongly curved backgrounds? In a generic background with string scale curvature, the notion of 0-form flux is not even defined. No signs of strong coupling in known massive IIA AdS solutions. UV completion of Sagai-Sugimoto still unknown, but the region between the D8 branes is not both weakly curved and at large coupling.

In some special cases, one might make sense out of a strongly curved, strongly coupled region in a massive IIA solution: If it were a part of a weakly curved solution, probably it will be small (string scale). If there were enough supersymmetry, it might be related by duality to a better description. For example T-dualizing to a background without F 0 flux. [Hull,…]

Massive IIA AdS duals of large N 3d CFTs To gain further insight into this result, will look at AdS vacua of massive IIA. This results in interesting statements about the dual field theories. We will find that the string coupling never grows large. At large N for fixed couplings, the behavior will be completely different than the massless case.

The N=6 CSM theory of N M2 branes in C 4 /Z k U(N) k x U(N) -k CSM with a pair of bifundamental hypermultiplets Field content: SU(2) x SU(2) global symmetry, which does not commute with SO(3) R, combining to form SU(4) R ( C I ) ¤ ; ( Ã I ) ¤ i n ( ¹ N ; N ) t h e i rcon j uga t es C I ; Ã I i n ( N ; ¹ N ) ma tt er ¯ e ld s A ¹ ; ~ A ¹ gauge ¯ e ld s C I = ( A a ; B ¤ _ a ) : W = 2 ¼ k ² a b ² _ a _ b ( A a B _ a A b B _ b )

Dual geometry The gauge theory coupling is 1/k. Fixing, the usual ‘t Hooft limit is a string theory. One obtains IIA on AdS 4 × CP 3 with N units of F 4 and k units of F 2 in CP 3 For, one finds small curvature and a large dilaton. Lifts to M-theory on ¸ = N = k, N ! 1 g IIA » ¸ 1 = 4 k R 2 s t r = 2 5 = 2 ¼ p ¸ N À k 5 A d S 4 £ S 7 = Z k

Massive IIA Consider deforming the N=6 CSM theory by the addition of a level a CS term for the second gauge group. In this theory the monopole operators corresponding to D0 branes develop a tadpole, since the induced electric charge (k, n 0 -k) cannot be cancelled with the matter fields. This motivates the idea that the total CS level should be related to the F 0 flux. [Gaiotto Tomasiello, Fujita Li Ryu Takayanagii] U ( N 1 ) k £ U ( N 2 ) ¡ k + n 0

The light U(1) on the moduli space has a level n 0 Chern-Simons term, matching the coupling of the D2 worldvolume to the Romans mass. For such deformations of N=6 CSM, there are field theories with N = 3,2,1,0 differing by the breaking of the SU(4) into flavor and R- symmetry. [Tomasiello; Gaiotto Tomasiello] k CS ( A 1 ) + ( n 0 ¡ k ) CS ( A 2 ) + j X j 2 ( A 1 ¡ A 2 ) 2

Review of massive AdS 4 solutions The dual geometries are topologically the same as the N=6 solution, but are now warped. Metric on CP 3 has SO(5), SO(4), SO(3) isometry in the N = 1,2,3 cases. Last solution only known perturbatively. d s 2 N = 1 ; 2 ; 3 = d s 2 warpe d A d S 4 + d s 2 CP 3 ; N = 1 ; 2 ; 3 n 0 = F 0 = k 1 ¡ k 2 n 2 = R CP 1 F 2 = k 2 n 4 = R CP 2 F 4 = N 2 ¡ N 1 n 6 = R CP 3 F 6 = N 1

Large N limit In the ‘t Hooft limit, these solutions are small deformations of the AdS 4 x CP 3 N=6 IIA supergravity solution. What about the large N limit for fixed levels? When n 0 = 0, this results in strong coupling, and a lift to M-theory. We now know that this is impossible for n 0 ≠ 0.

N=1 detailed analysis The SO(5) invariant metric on CP 3 is given by where the space is regarded as an S 2 bundle over S 4. where the space is regarded as an S 2 bundle over S 4. The parameter, where 2 is the Fubini- Study metric. d s 2 CP 3 ; N = 1 = R 2 ³ 1 8 ( d x i + ² ij k A j x k ) ¾ d s 2 S 4 ´ ¾ 2 [ 2 5 ; 2 ] R A d S = R 2 q 5 ( 2 ¾ + 1 ) B = ¡ p ( 2 ¡ ¾ )( ¾ ¡ 2 = 5 ) ¾ + 2 J + ¯

Parameters and fluxes The four parameters of the sugra solution are related to the quantized fluxes, R e ¡ B F k = n k ( 2 ¼ ` s ) k ¡ 1 ` ´ R A d S =( 2 ¼ ` s )

A new regime These relations can be inverted explicitly. Take n 4 = 0, n 2 = k, n 6 =N W h en N ¿ k 3 n 2 0 ¾ ! 2, t h e F u b i n i - S t u d yme t r i c, an d` » N 1 = 4 k 1 = 4, g s » N 1 = 4 k 5 = 4 d e f orma t i ono f t h e N = 6 so l u t i on. W h en N À k 3 n 2 0 ¾ ! 1, t h enear l y- K a hl erme t r i c, an d` » N 1 = 6 n 1 = 6 0, g s » 1 N 1 = 6 n 5 = 6 0 anewwea kl ycoup l e d reg i me !

Particle-like probe branes In the massive IIA solutions, D0 branes have a tadpole. Just as in the massless case, so do D2 branes, A D2/D0 bound state has a total worldvolume tadpole.. Take Consider n 0 =1, n 2 = k for simplicity. Then the mass of the D-brane is In the first phase, the D0s dominate the mass while in the second phase, the D2 dominates the mass D4 branes always exist, and have mass in AdS units, which is order N in both phases, as expected for a baryon. 1 2 ¼ ` s R F 2 ^ A D 2 ( n D 2 n 2 + n D 0 n 0 ) R R A » k 2 » N 2 = 3 L 5 g s n D 2 = n 0, n D 0 = ¡ n 2. L g s p k 2 + L 4.

Field theory interpretation Define the ‘t Hooft couplings, where n 4 =0 for simplicity. In these variables, the transition occurs for To have better control over the CFT, we turn to the N=2 case. ¸ 1 = N k 1 ; ¸ 2 = N ¡ k 2 ; ¸ § = ¸ 1 § ¸ 2 N » n 3 2 n 2 0 ) ¸ ¡ » ¸ 2 +

Light disorder operators in the CFT dual? There are clearly no light D-branes in this limit of the N=1 solution. One expects that the monopole operators of the CFT will get large quantum corrections to their dimensions. However, in the N=2 case, they are protected.

Monopoles operators There are monopole operators in YM-CS-matter theories, which we follow to the IR CSM. In radial quantization, it is a classical background with magnetic flux, and constant scalar,. Of course, in the CSM limit, It is crucial that the fields in μ are not charged under a. This operator creates a vortex. R S 2 F a = 2 ¼n ¾ = n = 2 [Borokhov Kapustin Wu] ¾ a = k ¡ 1 ¹

Anomalous dimension N=2 case We work in the UV to compute the 1-loop correction to the charge of a monopole operator under some flavor (or R–symmetry, or gauged) U(1). One finds This is an addition to the usual, mesonic charge of the operator. ¡ 1 2 P f erm i ons j q e j Q F

Monopoles in the massive duals Take Then Sits in an irrep with weight. Gauge invariant combinations with the matter fields require that In our case, take There are solutions to the equations: ¾ i = 1 2 d i ag ( w 1 i ;:::; w N i i ). n i = P w a i ( k i w 1 i ;:::; k i w N i i ) P k i n i = 0 w 2 = ( 1 ;::: k 1 :::; 1 ; 0 ;::: ) AA y ¡ B y B = k 1 2 ¼ w 1, BB y ¡ A y A = ¡ k 2 2 ¼ w 2. w 1 A = A w 2 ; w 2 B = B w 1 w 1 = ( 1 ;::: k 2 :::; 1 ; 0 ;::: ) an d

Dimensions There are two adjoint fermions with R-charge +1 in the vector multiplets, and four bi- fundamental fermions with R-charge -1/2. This results in a quantum correction to the R- charge of the monopole Combines with the matter dimension to give ( n 1 ¡ n 2 ) 2 ¡ ( N 1 ¡ N 2 )( n 1 ¡ n 2 ) k 1 k ( k 2 ¡ k 1 ) 2 ¡ ( k 2 ¡ k 1 )( N 1 ¡ N 2 )

N=2 solution The internal metric is SO(4) invariant. It has the form of T 1,1 fibered over an interval. One S 2 shrinks at each end. Depends on 4 parameters, L, g s, b,, where 0 is the undeformed solution. Related to the four quantized fluxes. d s 2 6 = e 2 B 1 ( t ) 4 d s 2 S e 2 B 2 ( t ) 4 d s 2 S ² 2 ( t ) d t ¡ 2 ( t )( d a + A 2 ¡ A 1 ) 2 Ã 1 2 [ 0 ; p 3 ]

N=2 solution The solution can be reduced to three first order differential equations. W h erew i = 4 e 2 B i ¡ 2 A, C t ; à = cos 2 ( 2 t ) cos 2 ( 2 à ) ¡ 1, e 2 A i s t h ewarp f ac t or o f t h e A d S me t r i c, an dà appears i n t h esp i nors.

The shape of the solution At each end of the interval one sphere shrinks. The size of the other at that point is plotted versus the deformation parameter. Develops a conifold singularity!

Two phases again Take n 4 = 0, n 2 = k, n 6 =N W h en N À k 3 n 2 0, Ã 1 ! p 3, acon i f o ld s i ngu l ar i t yappears, an d` » N 1 = 6 n 1 = 6 0, g s » 1 N 1 = 6 n 5 = 6 0. W h en N ¿ k 3 n 2 0, Ã 1 ! 0, ge t F u b i n i - S t u d yme t r i c, an d` » N 1 = 4 k 1 = 4, g s » N 1 = 4 k 5 = 4.

Match of light D2 branes A D2 brane wrapping the diagonal S 2 can be supersymmetric. The tadpole is cancelled by appropriate worldvolume flux. The mass can be calculated to give Remarkably, computing numerically, F is a constant, equal to 1. Precisely matches the field theory. m D 2 L = n 0 L ( 2 ¼ ) 2 g s ` 3 s R p d e t ( g + F ¡ B ) = ¡ n ¡ n 0 n 4 ¢ F ( Ã 1 )

A new weakly coupled string regime In the massive IIA solution dual to U(N) k × U(N) -k+n 0, we found This is in spite of the fact that the N=2 theory has light monopole operators. It would be interesting to understand the general behavior. R s t r » ³ N n 0 ´ 1 = 6 g s » 1 ( N n 5 0 ) 1 = 6 1 G N » N 5 = 3 n 1 = 3 0

Conclusions There are no strongly coupled solutions of massive IIA supergravity. Regions of strong curvature still need to be fully understood. Conifold singularities seen to arise in AdS backgrounds. The emergence of weakly coupled strings in a new regime of field theories.