What is(n t) the Strong Form of the Weak Gravity Conjecture

Transcription

1 What is(n t) the Strong Form of the Weak Gravity Conjecture Ben Heidenreich (Perimeter InsAtute) String Pheno 2017, July 3, 2017

2 Mo#va#on Complete QGs Swampland all gravita)onal EFTs 01/25

3 Example: No global symmetries M BHs??? M pl B L 02/25

4 Example: No global symmetries M BHs??? stable stable M pl B L 02/25

5 Example: No global symmetries M BHs??? stable stable infinite density of states! M pl B L 02/25

6 Conjecture Arkani-Hamed, Motl, Nicolis, Vafa 06 8 gauge force, 9 a charged pardcle with q/m q/m large extr. BH 03/25

7 Conjecture Arkani-Hamed, Motl, Nicolis, Vafa 06 8 gauge force, 9 a charged pardcle with q/m q/m large extr. BH Why? M BH region M Q BH decay allowed True in ST exs Q 03/25

8 Can BHs sa(sfy the WGC? L D=4 4 = a 1 (F µ F µ ) 2 + a 2 (F µ F µ ) 2 + a 3 F µ F C µ 04/25

9 Can BHs sa(sfy the WGC? L D=4 4 = a 1 (F µ F µ ) 2 + a 2 (F µ F µ ) 2 + a 3 F µ F C µ Yes No a a 3 > 0 a a 3 < 0 04/25

10 The Strong WGC (AMNV 06) Conjecture: The lightest charged parfcle is superextremal ( q/m q/m large extr. BH ) [See Brown, CoMrell, Shiu, Soler 15 for generalizafon to mulfple photons.] 05/25

11 The Strong WGC (AMNV 06) Conjecture: The lightest charged parfcle is superextremal ( q/m q/m large extr. BH ) [See Brown, CoMrell, Shiu, Soler 15 for generalizafon to mulfple photons.] This turns out to be false! [BH, Reece, Rudelius 16] 05/25

12 The Magne)c WGC Monopole self-energy m & Q2 e 2 WGC m< p 2 Q e M pl (AMNV 06) 1 =). em pl 06/25

13 What happens at? em pl? em pl light states 07/25

14 What happens at? em pl Typically many resonances e.g., string scale, KK scale, etc. em pl light states 07/25

15 The Convex Hull Condi/on Z 2 = Q 2 m stable (Cheung, Remmen 14) stable BH region Z 1 = Q 1 m 08/25

16 WGC consistency (BH, Reece, Rudelius 15) Q KK /m + BH region Q 5 /m 09/25

17 Q KK /m + 5d spectrum: BH region Q, m Q 5 /m 09/25

18 Q KK /m R! 0 + 5d spectrum: BH region Q, m Q 5 /m 09/25

19 Q KK /m + BH region 5d spectrum: 2Q, 2m Q, m Q 5 /m 09/25

20 WGC d 1 requires superextremal resonances of arbitrarily large charge! M Q 10/25

21 WGC d 1 requires superextremal resonances of arbitrarily large charge! Example: LaBce Weak Gravity Criterion: 8Q 2, 9 a superextremal charged parfcle 10/25

22 LWGC examples M KK theory D = 10 (e.g., D=10 IIA ST) M Het. ST m 2 = n2 R 2 Q Q m 2 = m 2 s(n + Q 2 /2 1) 11/25

23 Counterexamples KK theory on T 2 /(Z 2 Z 0 2) Z 2 : 1,2! 1,2 + Z 0 2 : 1! smooth (fixed pt free) orbifold! 1, 3! /25

24 conserved Z 2 : n 1 n 2 n 3! ( 1) n 1+n 2 n 1 n 2 n 3 not conserved! 13/25

25 conserved Z 2 : n 1 n 2 n 3! ( 1) n 1+n 2 n 1 n 2 n 3 not conserved! m 2 = n2 1 R n2 2 R n2 3 R 2 3 > n2 2 R n2 3 R 2 3 for n 2 2 2Z +1 n 2 =1 n 2 =2 13/25

26 String theory realiza/ons 1. IIA orien/fold T 3 /Z 2 Z IIA/B orbifold T 6 /Z 2 Z Het. T 4 /Z 2 orbifold (with Wilson lines) Qs /25

27 Strong WGC violated also! E.g., for R 1 R 2 >R 3 `s charged par@cle is subextremal! lightest m 2 lightest = 1 R R 2 2 > 1 R /25

28 Subla&ce WGC (slwgc) 9 a subla&ce of finite index 0 s.t. 8Q 2 0, 9 a superext. resonance Q 2 Q 1 16/25

29 Subla&ce WGC (slwgc) 9 a subla&ce of finite index 0 s.t. 8Q 2 0, 9 a superext. resonance True in known ST examples in D>4 Q 2 Q 1 16/25

30 slwgc from Modular Invariance (BH, Reece, Redulius 16; c.f. CoDrell, Shiu, Soler 16) Z =Tr(q L q R y QLȳ Q R ) q = e 2 i y = e 2 iµ = L 0 c 24 17/25

31 slwgc from Modular Invariance (BH, Reece, Redulius 16; c.f. CoDrell, Shiu, Soler 16) Z =Tr(q L q R y QLȳ Q R ) q = e 2 i y = e 2 iµ = L 0 c 24 17/25

32 Z(µ + ) =Z(µ) 8 2 µ2 ik Z(µ/, 1/ ) =e Z(µ, ) (Benjamin, Dyer, Fitzpatrick, Kachru 16) J a (z)j b (0) kab z /25

33 Z(µ + ) =Z(µ) 8 2 µ2 ik Z(µ/, 1/ ) =e Z(µ, ) (Benjamin, Dyer, Fitzpatrick, Kachru 16) J a (z)j b (0) kab z =) Z(µ + )=e 2 ikµ quasiperiod ik 2 Z(µ) 18/25

34 Z =Tr(q T Q2 y Q ) =Tr(q T (Q+k )2 y Q+k ) 19/25

35 Z =Tr(q T Q2 y Q ) =Tr(q T (Q+k )2 y Q+k ) = 0 4 M 2 k Q 19/25

36 Z =Tr(q T Q2 y Q ) =Tr(q T (Q+k )2 y Q+k ) = 0 4 M 2 extremal resonances q/m ext = ( q/m large BH ) k Q 19/25

37 How badly is the LWGC violated? Different measures: 1. Coarseness : p S ext 2. Index: / 0 3. Density: S ext / Orbifold Exs p apple 3 apple 256 & 50% S ext : LaGce sites with superext resonances 20/25

38 The (s)lwgc below Mpl Effec9ve QG scale: M e pl ' M pl / p N e 1/3 M pl 5eM pl 4eM pl 3eM pl 2eM pl em pl 21/25

39 The (s)lwgc below Mpl Effec9ve QG scale: M e pl ' M pl / p N e 1/3 M pl Landau pole: e!1 e 1/3 M pl Force unifica9on! 5eM pl 4eM pl 3eM pl 2eM pl em pl 21/25

40 Mul$ple (n) s M e pl e n n+2 Mpl e!1 ' e n n+2 Mpl Force unifica$on again! 22/25

41 The (s)lwgc above Mpl 4-deriv ops BH region M pl 23/25

42 (s)lwgc and axions A µ A M A 5 1 f = p 2 Re5 + S =2 Rm + A 5 (s)lwgc =) La3ce of superext. instantons 24/25

43 Conclusions Conven.onal strong WGC and variants are false! slwgc may hold in D>4 (modular inv.) Gives concrete explana.on for mag. WGC cutoff; causes force unifica.on Has consequences for axion poten.als 25/25