Complete spectrum of long operators in N=4 SYM at one loop

By N. Beisert, Vladimir Kazakov, Kazuhiro Sakai, K. Zarembo. 2005

144 citations recorded by the source corpus.

We construct the complete spectral curve for an arbitrary local operator, including fermions and covariant derivatives, of one-loop N=4 gauge theory in the thermodynamic limit. This curve perfectly reproduces the Frolov-Tseytlin limit of the full spectral curve of classical strings on AdS_5xS^5 derived in hep-th/0502226. To complete the comparison we introduce stacks, novel bound states of roots of different flavors which arise in the thermodynamic limit of the corresponding Bethe ansatz equations. We furthermore show the equivalence of various types of Bethe equations for the underlying su(2,2|4) superalgebra, in particular of the type "Beauty" and "Beast".

Subfields: Geometry and Topology, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/7f23031efe002bffc712ad995b36f8e90ad93c44

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Citations in the corpus

Five loop Konishi from AdS/CFT (2009, background): “the light-cone quantized Green-Schwartz superstring is currently almost completed. Historically, the developments which led to it concentrated on the Bethe Ansatz part mostly on the gauge theory side [11, 12, 13, 14, 15] as well as for classical string solutions in AdS5 × S5 [16, 17]. Later this was”
The analytic Bethe ansatz for a chain with centrally extended symmetry (2006, methodology): “It generalises the proposal in [44] for supersymmetric spin chains and takes the form Da = ( 1 − UaT1,aUa )( 1 − UaT2,aUa −1 1 − UaT3,aUa −1 1 − UaT4,aUa )”
The Algebraic Curve of Classical Superstrings on AdS5×S5 (2005, methodology): “Therefore also g(E1 ± E2)gST or g(E1 ± iE2)gST parametrize the coset as we can disentangle the contributions from E1 and E2 by projecting to the symmetric and antisymmetric parts.”
Integrability and the AdS3/CFT2 correspondence (2009, unknown): “In the Bethe-ansatz language branch points with composite monodromies correspond to stacks of Bethe roots [60] describing composite quantum states of several elementary excitations.”
Long-range psu(2,2|4) Bethe Ansatze for gauge theory and strings (2005, methodology): “In this limit, the duality transformation is a mere permutation Riemann sheets [14], so without loss of generality we can set η1 = η2 = +1.”
Beauty and the twist: the Bethe ansatz for twisted = 4 SYM (2005, methodology): “6 Here we cannot subtract 1 as in [ 25 ] (corresponding to a root at ∞ which we conventionally remove”
Four loop twist two, BFKL, wrapping and strings (2008, background): “The Bethe Ansatz Equations have been derived [12, 13, 14, 15, 16, 17, 18, 19] giving the spectrum of states with large quantum numbers.”
Gauge-string duality for (non)supersymmetric deformations of N=4 super-Yang–Mills theory (2005, background): “The discussion above can be thought of as an explicit implementation of the general arguments of [53] regarding the structures appearing in the thermodynamic limit of the N = 4 SYM spin chain.”
Four-loop perturbative Konishi from strings and finite size effects for multiparticle states (2008, background): “From this they conjectured the finite size correction coming both from the modification of the Bethe Ansatz and from the effect of the sea of particles and anti-particles.”
Supersymmetric Bethe ansatz and Baxter equations from discrete Hirota dynamics (2007, background): “the same solution for the T-functions T(a,s,u) ≡TK,M(a,s,u) at the highest level of the hierarchy. The diﬀerent systems of Bethe equations are known to be related by certain “duality transformations” [14, 45]. As we have seen in the main text, they admit a natural explanation in terms of a discrete ”