Small deformations of supersymmetric Wilson loops and open spin-chains
By N. Drukker, Shoichi Kawamoto. 2006
149 citations recorded by the source corpus.
We study insertions of composite operators into Wilson loops in = 4 supersymmetric Yang-Mills theory in four dimensions. The loops follow a circular or straight path and the composite insertions transform in the adjoint representation of the gauge group. This provides a gauge invariant way to define the correlator of non-singlet operators. Since the basic loop preserves an SL(2,) subgroup of the conformal group, we can assign a conformal dimension to those insertions and calculate the corrections to the classical dimension in perturbation theory. The calculation turns out to be very similar to that of single-trace local operators and may also be expressed in terms of a spin-chain. In this case the spin-chain is open and at one-loop order has Neumann boundary conditions on the type of scalar insertions that we consider. This system is integrable and we write the Bethe ansatz describing it. We compare the spectrum in the limit of large angular momentum both in the dilute gas approximation and the thermodynamic limit to the relevant string solution in the BMN limit and in the full AdS5 × S5 metric and find agreement.
Subfields: Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/f219c47ee538520a4813df1593811ccb17aff4d6
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In Nuclear and High Energy Physics
Citations in the corpus
- The quark anti-quark potential and the cusp anomalous dimension from a TBA equation (2012, methodology): “These equations describe magnons moving on a long strip of length L with two boundaries associated to the Wilson loop on each of the “sides” of the operator, see [11].”
- Supersymmetric Wilson loops on S**3. (2007, unknown): “Then if one considers two local deformations of the line or circle they can be analyzed again using spin-chain techniques [33].”
- Comments on gluon scattering amplitudes via AdS/CFT (2007, background): “Then the insertion of the operators φ(1), · · · , φ(5) corresponds to BPS operators of dimension ∆ = 1, see the discussion in [22].”
- Integrable Wilson loops (2012, methodology): “The boundary interactions were calculated in [21] only in the SU(2) sector and only at one loop, where they are essentially trivial.”
- Generalized quark-antiquark potential at weak and strong coupling (2011, background): “The Wilson loop with one Z and one Z̄ insertion is BPS (unless the insertions are coincident), and receives no divergent quantum corrections [29].”
- 1/4 BPS circular loops, unstable world-sheet instantons and the matrix model (2006, background): “Those include the ones studied in this paper as well as some deformations of the line or circle by insertion of local operators as in [21].”