Codimension2 Solutions in 5 D Supergravity Masaki Shigemori

Codimension-2 Solutions in 5 D Supergravity Masaki Shigemori (YITP Kyoto) Minkyu Park & MS, ar. Xiv: 1505. 05169 August 14, 2015 CERN-CKC TH Institute on Duality Symmetries in String and M-Theories

Introduction

Low codim branes (1) 3 Peculiar, but all the more interesting!

Low codim branes (2) Why interesting? �F-theory �Exotic, non-geometric in general [de Boer+Shigemori ’ 10, ’ 12] codim 2 brane U-duality monodromy Metric not single-valued Naturally lives in DFT/EFT 4

Low codim branes (3) �Can be created out of ordinary branes spontaneously polarize D 6 D 2 “supertube transition” �More common than previously thought �Relevance for black hole physics Cf. Fuzzball proposal, Microstate geometry program 5

Multi-center solutions � codim-3 source Paradigm for BH physics Split attractor flow, wall crossing, quiver QM… � Microstate geometry program � 6

Codim-2 solutions multi-valued. New solutions! Various applications � New microstates (MGP) � 7

Goal: �Demonstrate that these codim-2 solutions exist by presenting some simple but explicit examples �We will see monodromy structure characteristic of codim-2 branes 8

4 D/5 D Solutions

Setup � �Action 10

BPS solutions [Gutowski-Reall ’ 04] [Bena-Warner ’ 04] [Gutowski-Gauntlett ’ 04] � Bates-Denef/Gutowski-Gauntlett/Bena-Warner solution, or “ 4 D/5 D solution” 11

Multi-center solution 12

Integrability cond. � 13

10 D IIA fields … 14

Torus moduli 15

Example: 4 -charge BH �Susy BH in 4 D (4 supercharges) �Single-center 16

Microstate geometry program What portion of the BH entropy of supersymmetric BHs is accounted for by smooth, horizonless solutions of classical sugra? M-circle BH smooth multi-center solution � 4 D/5 D solution: paradigm for MGP [Bena, Warner ’ 06] [Berglund, Gimon, Levi ’ 06] � Not enough microstates found so [Bena, Bobev, Giusto, Ruef, Warner ’ 11] [de Boer, El-Showk, Messamah, Van den far Bleeken ’ 09] 17

Supertube transition

Supertube transition [Mateos+Townsend 2001] polarize F 1(9) D 0 � Spontaneous polarization phenomenon � Produces new dipole charge � Cross section = arbitrary curve 19 (cf. Myers effect)

F 1 -P frame polarize � 20 F 1(9) P wiggly F 1

Dualizing supertubes Original supertube effect: dualize! � Constituents of 4 -chg BH! � Need to incorporate codim-2 objects in 4 D/5 D sol’n 21

Sol’n with codim-2 centers 22

NS 5 1 2 3 4 5 6 7 8 9 ∙ ∙ O O O ~ ~ KKM 1 2 3 4 5 6 7 8 9 ∙ ∙ O O O ⦿ ~ 1 2 3 4 5 6 7 8 9 ∙ ∙ O O O ⦿ ⦿ 23

Codim-2 solutions (1)

Straight config (1) 25

Straight config (2) � NS 5(34567) charge � Metric is single-valued (no exotic brane, NS 5 only) 4 D modulus: 26

NS 5 along general curve: 27

� Obtained by dualizing known supertube solution E. g. [Emparan+Mateos+Townsend ’ 01] � Integrability condition satisfied 28

� 10 D metric is single- valued � Torus moduli 29 NS 5 charge

30

� 10 D metric: multi-valued 31 T-duality twist

�Torus moduli T-dual modulus: 32

Summary so far �Codim-2 solutions exist �Constituents of BH systems must be important for BH physics 33

Codim-2 solutions (2)

More general solutions? �Need to find harmonic functions such that… Give desired monodromy for moduli etc. Cf. F-theory Give single/multi-valued metric as necessary Satisfies integrability condition �Difficult in general 35

2 -dipole solution 36

37

� Obtained by smearing and dualizing “superthread” [Niehoff+Vasilakis+Warner solution ’ 12] � Correct monodromy for NS 5 38

3 -dipole solution �Can be found, but more complicated and implicit 39

More dipoles �Represents microstates of 4 -charge BH �Difficult to find…not successful so far 40

Mixed configurations

Codim-2 & codim-3 42

Integrability condition (a) (b) (c) Easy to satisfy 43

Conclusions

Conclusions � 4 D/5 D solution: a paradigm for BH research �Only codim-3 solutions studied so far �Codim-2 solutions also important Scratched the surface Interesting dynamics General solutions? 45

Future directions �Applications Split attractor flow, wall crossing, quiver QM Microstate Geometry Program �Lower codimension Superstratum �Connect to DFT/EFT Brane charge and flux formulation More general non-geometric sol’ns? Add your own 46 codim-2 brane SS twist

Thanks!