Chern-Simons-Matter Theories, High-Spin Gravity, and 3D Bosonization Guy Gur-Ari Weizmann Institute, Israel The Galileo Galilei Institute, Florence, May 2013 [Aharony, GA, Yacoby 2011, 2012] [GA, Yacoby 2012] [Aharony, Giombi, GA, Maldacena, Yacoby 2012]
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Chern-Simons-Matter Theories, High-Spin Gravity,
and 3D Bosonization
Guy Gur-AriWeizmann Institute, Israel
The Galileo Galilei Institute, Florence, May 2013[Aharony, GA, Yacoby 2011, 2012] [GA, Yacoby 2012][Aharony, Giombi, GA, Maldacena, Yacoby 2012]
Vector Models in 3D
• Complex scalars
• Singlet sector of
• Single-trace primaries:
i = 1, . . . , N
s = 0, 1, 2, . . .Js = �†
i@ · · · @�i
U(N)
�s = s+ 1
L = @µ�†i@µ�
i +�6
N2(�†
i�i)3
• Singlet sector of
• Single-trace primaries:
Vector Models in 3DL = i�
µ@µ i
J0 = Js = �@ · · · @ �0 = 2
�s = s+ 1
s = 1, 2, . . .
U(N)
Outline
• 3D vector models ↔ high-spin gravity
• Matter + Chern-Simons interactions
• 3D bosonization
Vasiliev’s Theory
• Defined on AdS4
• Scalar, photon, graviton, ...
• Consistent, classical interacting theory
dx
A+ A ⇤ A =
1
4+ ei✓0B ⇤K
�dz2 + c.c.
dx
B + A ⇤B �B ⇤ ⇡(A) = 0
Holographic Duality
[Sezgin, Sundell 2001]
GN ⇠ 1
NJ0, Js ! B, A ✓0 = 0
✓0 = ⇡/2
Boundary scalars:
Boundary fermions:
• dimension:
• Currents not renormalized at large N
• Bulk: change of scalar boundary conditions
Critical Vector Model
Wilson-Fischer
[Klebanov, Polyakov 2002]
Free Scalars�L ⇠ (�†�)2
J0 �IR0 = d��0 = 2
Detailed Evidence
• Conformal theory in flat 3D space + high-spin symmetry ⇒ free theory[Maldacena, Zhiboedov 2011]
• All 3-point functions agree[Giombi, Yin 2010]
Motivation• Weak-weak duality
• Tensionless limit of string theory[Chang, Minwalla, Sharma, Yin 2012]
• Boundary scalars and fermions continuously connected