On the logarithmic powers of sl(2) SYM(4)
Nov, 2009
Citations per year
Abstract: (Elsevier)
In the high spin limit the minimal anomalous dimension of (fixed) twist operators in the sl ( 2 ) sector of planar N = 4 Super Yang–Mills theory expands as γ ( g , s , L ) = f ( g ) ln s + f sl ( g , L ) + ∑ n = 1 ∞ γ ( n ) ( g , L ) × ( ln s ) − n + ⋯ . We find that the sub-logarithmic contribution γ ( n ) ( g , L ) is governed by a linear integral equation, depending on the solution of the linear integral equations appearing at the steps n ′ ⩽ n − 3 . We work out this recursive procedure and determine explicitly γ ( n ) ( g , L ) (in particular γ ( 1 ) ( g , L ) = 0 and γ ( n ) ( g , 2 ) = γ ( n ) ( g , 3 ) = 0 ). Furthermore, we connect the γ ( n ) ( g , L ) (for finite L ) to the generalised scaling functions, f n ( r ) ( g ) , appearing in the limit of large twist L ∼ ln s . Finally, we provide the first orders of weak and strong coupling for the first γ ( n ) ( g , L ) (and hence f n ( r ) ( g ) ).Note:
- 15 pages, added references, minor changes in introduction and conclusion
- Integrability
- Infinite conserved charges
- Bethe Ansatz equations
- AdS-CFT correspondence
- operator: twist
- integral equations
- anomalous dimension
- strong coupling
- gauge field theory: Yang-Mills
- SL(2)
References(48)
Figures(0)