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Conference on Integrability in Gauge and String Theory 2010
Conference on Integrability in Gauge and String Theory 2010
from 28 June 2010 to 02 July 2010 Nordita
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TBA and functional relations for the AdS_5/CFT_4 correspondence
The exact anomalous dimensions of the single trace 
composite operators in the planar limit of $N=4$ super 
Yang-Mills can be studied in the framework of the 
Thermodynamic Bethe Ansatz method (TBA). In this 
talk, I will discuss the analytic properties of the TBA 
solutions -the Y-functions- and the  associated set of 
functional relations -the Y-system-. 
Contrary to the more studied relativistic invariant cases, the  
$AdS_5/CFT_4$-related Y-functions live on multi-sheeted 
coverings of the complex plane with an infinite number of 
square-root branch points.

As a direct consequence of this fact, the  TBA  equations 
and in particular  the dressing kernel cannot  be obtained 
from the Y-system without extra information on the 
square-root discontinuities across semi-infinite segments in 
the complex plane.
It is shown that the discontinuity functions fulfill an 
independent simple set of  local functional equations.
The Y-system extended by the discontinuity relations forms 
a fundamental set of local non-linear constraints that can 
be easily transformed into integral form through Cauchy's 
Id: 259
Place: Nordita
Room: Oskar Klein lecture hall
Starting date:
29-Jun-2010   14:30
Duration: 01h00'
Presenters: TATEO, Roberto
Material: slide Slides

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