holography of wilson-loop expectation values with local operator insertions
DESCRIPTION
Holography of Wilson-loop expectation values with local operator insertions. Akitsugu Miwa ( Univ. of Tokyo, Komaba ) work in collaboration with Tamiaki Yoneya based on hep-th/0609007. 4-dim, 4, SU(N), SYM. IIB superstring on. AdS 5. boundary. - PowerPoint PPT PresentationTRANSCRIPT
Holography of Wilson-loop expectation valuesHolography of Wilson-loop expectation values
with local operator insertionswith local operator insertions Akitsugu Miwa ( Univ. of Tokyo, Komaba )
work in collaboration with Tamiaki Yoneya
based on hep-th/0609007
introduction and motivationJ.M.Maldacena(1997)AdS/CFT correspondence:AdS/CFT correspondence:
present status and aim of this talk:present status and aim of this talk:
generic loop: difficult
circle, straight line: well studied
small deformation of circle or straight line
status
this talk
4-dim, 4, SU(N), SYM IIB superstring on
Wilson loop in AdS/CFT:Wilson loop in AdS/CFT: S.J.Rey, J.Yee(1998), J.M. Maldacena(1998)
Wilson loop string world sheet
boundary
AdS5
deformation of loop and local operator insertion:deformation of loop and local operator insertion:
Wilson loop:
deformation of loop:
large R-charge local operator insertions:large R-charge local operator insertions: N. Drukker S. Kawamoto (2006)
corresponding string world sheet:corresponding string world sheet:
we consider: string world sheet with large angular momentum
SO(6) symmetry:SO(6) symmetry:
large R-charge
gauge theory side
R symmetry : SO(6): ( rotation of 6 scalars )
U(1) sub-group: rotation of a phase of
string theory side
isometry on S5 : SO(6)
U(1) sub-group: rotation in 5-6 plain
4
5 6
question:question:
SYM side:
string side: near boundary separated from boundary?
path of large angular momentum mode:path of large angular momentum mode:
classical path do not reach the boundarybecause of a potential barrier
potential barrier
path of large angular momentum mode
tunneling geodesic:tunneling geodesic: S.Dobashi, H.Shimada, T.Yoneya (2002)
we will study string world sheet around tunneling geodesic
today’s talk:today’s talk:
we want VEV of Wilson loop:
path of localized angular momentum
potential barrier
tunneling solution
correlation function of large R-charge local operators
ex:
4
5 6
some comments
stringstring action:action:
AdS/CFT correspondence:AdS/CFT correspondence:
semi-classical approximation:semi-classical approximation:
large ‘t Hooft coupling in SYM
semi-classical approximation of string theory requires large
plan of the talk
• introduction and motivation
• world sheet with large angular momentum
• evaluation of “area” of world sheets
• interpretation of results
• conclusion and future work
world sheet with large angular momentum
SS55 part: part:solution: patch1
patch2
metricmetric::
path of localized angular momentum
AdSAdS55 part: part:
Hamiltonian constraint, EOM:
boundary
path of localized angular momentum
tunneling solution:tunneling solution: S.Dobashi, H.Shimada, T.Yoneya (2002)
tunneling solution (path of localized R-charge)
world sheet
we want:we want:
attached to a loop on the boundary
propagating along the tunneling geodesic
N.Drukker, S.Kawamoto (2006)comment on non-tunneling solution:comment on non-tunneling solution:
If we use non-tunneling solution, it is difficult to check following relation:
full world-sheet solution:full world-sheet solution:
tunneling geodesic
circle with radius
full world-sheet solution:full world-sheet solution:
corresponding Wilson loop:corresponding Wilson loop:
evaluation of “area” of world sheets
N.Drukker, D.Gross, H.Ooguri (1999)““area” of a world sheetarea” of a world sheet
two cutoff schemestwo cutoff schemes
target-space cutoff:
world-sheet cutoff:
w.s. cutoff can be rewritten as:
divergences:divergences:
singular behavior of the metric .
infinite extension of the world sheet .
(const. depends on regularization schemes)
results:results:
consistent with ladder graph calculation
interpretation of results
in our casein our case
consistent with our result
ladder graphladder graph (planar graph without internal vertex):(planar graph without internal vertex):
D.Berenstein, R.Corrado, W. Fischler, J.M.Maldacena (1998),N.Drukker, D.J.Gross, H. Ooguri (1999),J.K.Erickson, G.W.Semenoff, K.Zarembo (2000), etc.
not laddercircle:
straight line:
These results are known to be consistent with the calculation of the area of world sheet without angular momentum.
conclusion and future work
future work:future work:
more complicated local operator insertions (more complicated deformation of string world sheet)
conclusion:conclusion:
open string solution around the tunneling geodesic,
the “area” of the world sheet in two cutoff schemes.
We have studied
Main results are
( consistent with ladder graph calculation )
and independent finite terms depend on cutoff schemes
Wilson loop in AdS/CFTS.J.Rey, J.Yee(1998); J.M.Maldacena(1998)
conjecture:conjecture:
SYM side:SYM side:Wilson loop
string side:string side:
flat
string world sheet
about Wilson loop
localized R-charge
introduction and motivation
J.M.Maldacena(1997)AdS/CFT correspondence:AdS/CFT correspondence:
4-dim, 4, SU(N), SYM IIB superstring on
N D3-brane system
flat
boundary
present status and the aim of this talk:present status and the aim of this talk:
generic loop: difficult
circle, straight line: well studied
small deformation of circle or straight line
status
this talk
Wilson loop in AdS/CFT:Wilson loop in AdS/CFT: S.J.Rey, J.Yee(1998), J.M. Maldacena(1998)
Wilson loop string world sheet
boundary
AdS5
introduction and motivation