enhancing and double field theory
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Enhancing and Double Field Theory G . A l d a z a b a l , - PowerPoint PPT Presentation

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Enhancing and Double Field Theory G . A l d a z a b a l , C A B - I B , B a r i l o c h e S t r i n g y G e o m e t r y , M I T P , 2 0 1 5 I n c o l l a b o r a t i o n w i t h

  1. P L A N ● S t r i n g : ( 3 - p o i n t ) s c a t t e r i n g a m p l i t u d e s f o r a n d D e r i v a t i o n o f E fg e c t i v e g a u g e fj e l d t h e o r y a c t i o n ● D F T : B r i e f i n t r o d u c t i o n . F r a m e f o r m u l a t i o n . D e r i v a t i o n o f g e n e r i c E fg e c t i v e D F T g a u g e fj e l d t h e o r y a c t i o n .

  2. P L A N ● S t r i n g : ( 3 - p o i n t ) s c a t t e r i n g a m p l i t u d e s f o r a n d D e r i v a t i o n o f E fg e c t i v e g a u g e fj e l d t h e o r y a c t i o n ● D F T : B r i e f i n t r o d u c t i o n . F r a m e f o r m u l a t i o n . D e r i v a t i o n o f g e n e r i c E fg e c t i v e D F T g a u g e fj e l d t h e o r y a c t i o n . ● B u i l d u p a s p e c i fj c f r a m e a n d c o m p a r e w i t h s t r i n g s r e s u l t s .

  3. P L A N ● S t r i n g : ( 3 - p o i n t ) s c a t t e r i n g a m p l i t u d e s f o r a n d D e r i v a t i o n o f E fg e c t i v e g a u g e fj e l d t h e o r y a c t i o n ● D F T : B r i e f i n t r o d u c t i o n . F r a m e f o r m u l a t i o n . D e r i v a t i o n o f g e n e r i c E fg e c t i v e D F T g a u g e fj e l d t h e o r y a c t i o n . ● B u i l d u p a s p e c i fj c f r a m e a n d c o m p a r e w i t h s t r i n g s r e s u l t s .

  4. P L A N ● S t r i n g : ( 3 - p o i n t ) s c a t t e r i n g a m p l i t u d e s f o r a n d D e r i v a t i o n o f E fg e c t i v e g a u g e fj e l d t h e o r y a c t i o n ● D F T : B r i e f i n t r o d u c t i o n . F r a m e f o r m u l a t i o n . D e r i v a t i o n o f g e n e r i c E fg e c t i v e D F T g a u g e fj e l d t h e o r y a c t i o n . ● B u i l d u p a s p e c i fj c f r a m e a n d c o m p a r e w i t h s t r i n g s r e s u l t s . ● C o m p a c t i fj c a t i o n s p a c e G e o m e t r y ( m o r e w i t h M a r i a n a G r a ñ a )

  5. P L A N ● S t r i n g : ( 3 - p o i n t ) s c a t t e r i n g a m p l i t u d e s f o r a n d D e r i v a t i o n o f E fg e c t i v e g a u g e fj e l d t h e o r y a c t i o n ● D F T : B r i e f i n t r o d u c t i o n . F r a m e f o r m u l a t i o n . D e r i v a t i o n o f g e n e r i c E fg e c t i v e D F T g a u g e fj e l d t h e o r y a c t i o n . ● B u i l d u p a s p e c i fj c f r a m e a n d c o m p a r e w i t h s t r i n g s r e s u l t s . ● C o m p a c t i fj c a t i o n s p a c e G e o m e t r y ( m o r e w i t h M a r i a n a G r a ñ a )

  6. P L A N ● S t r i n g : ( 3 - p o i n t ) s c a t t e r i n g a m p l i t u d e s f o r a n d D e r i v a t i o n o f E fg e c t i v e g a u g e fj e l d t h e o r y a c t i o n ● D F T : B r i e f i n t r o d u c t i o n . F r a m e f o r m u l a t i o n . D e r i v a t i o n o f g e n e r i c E fg e c t i v e D F T g a u g e fj e l d t h e o r y a c t i o n . ● B u i l d u p a s p e c i fj c f r a m e a n d c o m p a r e w i t h s t r i n g s r e s u l t s . ● C o m p a c t i fj c a t i o n s p a c e G e o m e t r y ( m o r e w i t h M a r i a n a G r a ñ a ) ● C o n c l u s i o n s a n d O u t l o o k

  7. P L A N ● S t r i n g : ( 3 - p o i n t ) s c a t t e r i n g a m p l i t u d e s f o r a n d D e r i v a t i o n o f E fg e c t i v e g a u g e fj e l d t h e o r y a c t i o n ● D F T : B r i e f i n t r o d u c t i o n . F r a m e f o r m u l a t i o n . D e r i v a t i o n o f g e n e r i c E fg e c t i v e D F T g a u g e fj e l d t h e o r y a c t i o n . ● B u i l d u p a s p e c i fj c f r a m e a n d c o m p a r e w i t h s t r i n g s r e s u l t s . ● C o m p a c t i fj c a t i o n s p a c e G e o m e t r y ( m o r e w i t h M a r i a n a G r a ñ a ) ● C o n c l u s i o n s a n d O u t l o o k

  8. S t r i n g t h e o r y a c t i o n

  9. S t r i n g v e r t e x o p e r a t o r s

  10. S t r i n g v e r t e x o p e r a t o r s m i x e s L e f t a n d R i g h t

  11. S t r i n g v e r t e x o p e r a t o r s m i x e s L e f t a n d R i g h t L e v e l m a t c h i n g

  12. S t r i n g v e r t e x o p e r a t o r s m i x e s L e f t a n d R i g h t L e v e l m a t c h i n g i . e .

  13. S t r i n g v e r t e x o p e r a t o r s m i x e s L e f t a n d R i g h t L e v e l m a t c h i n g i . e . M a s s i v e v e c t o r

  15. o r s o p e r a t v e r t e x S t r i n g

  16. o r s o p e r a t v e r t e x S t r i n g ● M a s s l e s s L e f t g a u g e b o s o n s

  17. o r s o p e r a t v e r t e x S t r i n g ● M a s s l e s s L e f t g a u g e b o s o n s

  18. o r s o p e r a t v e r t e x S t r i n g ● M a s s l e s s L e f t g a u g e b o s o n s ● M a s s l e s s R i g h t g a u g e b o s o n s

  19. o r s o p e r a t v e r t e x S t r i n g ● M a s s l e s s L e f t g a u g e b o s o n s ● M a s s l e s s R i g h t g a u g e b o s o n s ● M a s s l e s s s c a l a r s

  20. C F T C u r r e n t s

  21. C F T C u r r e n t s

  22. C F T C u r r e n t s

  23. C F T C u r r e n t s M o d e e x p a n s i o n

  24. C F T C u r r e n t s M o d e e x p a n s i o n

  25. C F T C u r r e n t s M o d e e x p a n s i o n I n t e r n a l b a s e

  26. C F T C u r r e n t s M o d e e x p a n s i o n I n t e r n a l b a s e

  27. C F T C u r r e n t s M o d e e x p a n s i o n I n t e r n a l b a s e

  28. C F T C u r r e n t s M o d e e x p a n s i o n I n t e r n a l b a s e N o s t r o n g c o n s t r a i n t

  29. t u d e s a m p l i 3 - p o i n t S t r i n g g r a v i t y s e c t o r g a u g e k i n e t i c t e r m s s c a l a r k i n e t i c t e r m s c u b i c s c a l a r p o t e t i a l m i x i n g s

  30. E fg e c t i v e a c t i o n

  32. o r s o p e r a t v e r t e x S t r i n g O n l y fj e l d t h a t a r e m a s s l e s a t

  33. o r s o p e r a t v e r t e x S t r i n g O n l y fj e l d t h a t a r e m a s s l e s a t i . e .

  34. o r s o p e r a t v e r t e x S t r i n g O n l y fj e l d t h a t a r e m a s s l e s a t i . e . a n o m a l o u s

  35. o r s o p e r a t v e r t e x S t r i n g O n l y fj e l d t h a t a r e m a s s l e s a t i . e . a n o m a l o u s

  36. o r s o p e r a t v e r t e x S t r i n g O n l y fj e l d t h a t a r e m a s s l e s a t i . e . a n o m a l o u s G o l d s t o n e b o s o n M a s s i v e v e c t o r b o s o n

  37. o r s o p e r a t v e r t e x S t r i n g O n l y fj e l d t h a t a r e m a s s l e s a t i . e . a n o m a l o u s G o l d s t o n e b o s o n M a s s i v e v e c t o r b o s o n A n o m a l y c a n c e l l a t i o n , l o n g i t u d i n a l p o l a r i z a t i o n ' t H o o f t g a u g e fj x i n g

  38. E fg e c t i v e a c t i o n

  39. Effective theory with massless and “slightly massive” states “Hidden” T-duality symmetry

  40. c a n b e u n d e r s t o o d f r o m H i g g s m e c h a n i s m Same degrees of freedom as in F u l l d e p e n d e n c e o n I n d i c a t e s c o n t r i b u t i o n s c o m i n g f r o m h i g h e r o r d e r “ n o n r e n o r m a l i z a b l e ” t e r m s

  41. S y m m e t r y b r e a k i n g . . . I n d i c a t e s w i t h

  42. D F T a c t i o n

  43. P L A N

  44. P L A N ● B r i e f i n t r o d u c t i o n D F T f r a m e f o r m u l a t i o n .

  45. P L A N ● B r i e f i n t r o d u c t i o n D F T f r a m e f o r m u l a t i o n . D F T g e n e r a l i z e d S c h e r k - S c h w a r z c o m p a c t i fj c a t i o n .

  46. P L A N ● B r i e f i n t r o d u c t i o n D F T f r a m e f o r m u l a t i o n . D F T g e n e r a l i z e d S c h e r k - S c h w a r z c o m p a c t i fj c a t i o n . G e n e r a l E fg e c t i v e D F T g a u g e fj e l d t h e o r y a c t i o n

  47. P L A N ● B r i e f i n t r o d u c t i o n D F T f r a m e f o r m u l a t i o n . D F T g e n e r a l i z e d S c h e r k - S c h w a r z c o m p a c t i fj c a t i o n . G e n e r a l E fg e c t i v e D F T g a u g e fj e l d t h e o r y a c t i o n

  48. P L A N ● B r i e f i n t r o d u c t i o n D F T f r a m e f o r m u l a t i o n . D F T g e n e r a l i z e d S c h e r k - S c h w a r z c o m p a c t i fj c a t i o n . G e n e r a l E fg e c t i v e D F T g a u g e fj e l d t h e o r y a c t i o n ● w a r m i n g u p K K c i r c l e r e d u c t i o n

  49. P L A N ● B r i e f i n t r o d u c t i o n D F T f r a m e f o r m u l a t i o n . D F T g e n e r a l i z e d S c h e r k - S c h w a r z c o m p a c t i fj c a t i o n . G e n e r a l E fg e c t i v e D F T g a u g e fj e l d t h e o r y a c t i o n ● w a r m i n g u p K K c i r c l e r e d u c t i o n ● G e n e r a l i z a t i o n t o d e s c r i b e e n h a n c i n g t o

  50. P L A N ● B r i e f i n t r o d u c t i o n D F T f r a m e f o r m u l a t i o n . D F T g e n e r a l i z e d S c h e r k - S c h w a r z c o m p a c t i fj c a t i o n . G e n e r a l E fg e c t i v e D F T g a u g e fj e l d t h e o r y a c t i o n ● w a r m i n g u p K K c i r c l e r e d u c t i o n ● G e n e r a l i z a t i o n t o d e s c r i b e e n h a n c i n g t o ● E fg e c t i v e D F T g a u g e fj e l d t h e o r y a c t i o n

  51. D F T

  52. D F T ● c o o r d i n a t e s

  53. D F T ● c o o r d i n a t e s ● fj e l d s

  54. D F T ● c o o r d i n a t e s ● fj e l d s ● S y m m e t r i e s

  55. D F T ● c o o r d i n a t e s d u a l c o o r d i n a t e s i n t e r n a l , f u n d a m e n t a l r e p r e s e n t a t i o n o f ● fj e l d s ● S y m m e t r i e s

  56. D F T ● c o o r d i n a t e s d u a l c o o r d i n a t e s i n t e r n a l , f u n d a m e n t a l r e p r e s e n t a t i o n o f ● fj e l d s r e s t r i c t t o G e n e r a l i z e d m e t r i c d i l a t o n ● S y m m e t r i e s

  57. D F T ● c o o r d i n a t e s d u a l c o o r d i n a t e s i n t e r n a l , f u n d a m e n t a l r e p r e s e n t a t i o n o f ● fj e l d s r e s t r i c t t o G e n e r a l i z e d m e t r i c d i l a t o n ● S y m m e t r i e s

  58. D F T ● c o o r d i n a t e s d u a l c o o r d i n a t e s i n t e r n a l , f u n d a m e n t a l r e p r e s e n t a t i o n o f ● fj e l d s r e s t r i c t t o G e n e r a l i z e d m e t r i c d i l a t o n ● S y m m e t r i e s

  59. D F T ● c o o r d i n a t e s d u a l c o o r d i n a t e s i n t e r n a l , f u n d a m e n t a l r e p r e s e n t a t i o n o f ● fj e l d s r e s t r i c t t o G e n e r a l i z e d m e t r i c d i l a t o n ● S y m m e t r i e s

  60. D F T ● c o o r d i n a t e s d u a l c o o r d i n a t e s i n t e r n a l , f u n d a m e n t a l r e p r e s e n t a t i o n o f ● fj e l d s r e s t r i c t t o G e n e r a l i z e d m e t r i c d i l a t o n ● S y m m e t r i e s c o n s t r a i n t s c l o s u r e +

  61. D F T ● c o o r d i n a t e s d u a l c o o r d i n a t e s i n t e r n a l , f u n d a m e n t a l r e p r e s e n t a t i o n o f ● fj e l d s r e s t r i c t t o G e n e r a l i z e d m e t r i c d i l a t o n ● S y m m e t r i e s c o n s t r a i n t s . c l o s u r e + i . e

  62. D F T F r a m e f o r m u l a t i o n : Geissbuhler, (2011) v e c t o r s + f o r m s Marques, Nuñez, Penas, G.A, Marques, Nuñez (2014) g e n e r a l i z e d f r a m e g e n e r a l i z e d m e t r i c c a n b e p a r a m e t r i z e d a s a n d w i t h

  63. D F T G e n e r a l i z e d ( d y n a m i c a l ) fm u x e s t r a n s f o r m s a s a v e c t o r i n p a r t i c u l a r F l u x e s ( d y n a m i c a l ) s c a l a r i f c l o s u r e i s s a t i s fj e d

  64. D F T a c t i o n

  65. S c h e r k - S c h w a r z d i m e n s i o n a l r e d u c t i o n s G. A, Baron, Marques, Nuñez, (2011) Geissbuller frame twist g a u g e d Q u a d r a t i c c o n s t a n t c o n s t r a i n t s

  66. D F T E fg e c t i v e a c t i o n s c a l a r s

  67. I s t h e r e a D F T f r a m e ?

  68. Wa r m i n g u p K K r e d u c t i o n o n a c i r c l e

  69. C i r c l e K K r e d u c t i o n G e n e r a l i z e d f r a m e

  70. C i r c l e r e d u c t i o n I n t e r n a l f r a m e S c h e r k - S c h w a r z M e t r i c fm u c t u a t i o n s

  71. C i r c l e r e d u c t i o n

  72. C i r c l e r e d u c t i o n

  73. C i r c l e r e d u c t i o n s c a l a r m a t r i x

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