A defect action for Wilson loops

We study the 1-loop dilatation operator for insertions of composite operators in a generalized Wilson loop in N = 4 super Yang-Mills, which interpolates between the supersymmetric Wilson-Maldacena loop and the ordinary Wilson loop with no scalar coupling. For SO(6) scalar insertions, we show that the 1-loop dilatation operator is integrable for the endpoints of the interpolation, i.e. either for the Wilson-Maldacena or the ordinary Wilson loop. Moreover, we also show that integrability persists for SU (2|3) insertions in the ordinary Wilson loop, even when the term making the spin chain length dynamical is included.

Section: One Loop Bulk and Boundary Dilatation Operatorsupporting

confidence: 78%

“…There they were also able to use the Wilson loop expectation value to determine the leading order of structure constants appearing in the three point function (1.6) for the Φ 4 operator. For recent works in non-supersymmetric Wilson loops and underlying defect CFTs see [19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Spin chain integrability in non-supersymmetric Wilson loops

Correa

Leoni

Luque

2018

“…one gets a novel example of the AdS 2 /CFT 1 duality. This CFT 1 , which is "induced" from the 4d CFT on the 1d defect, is not expected to have a description based on a local 1d Lagrangian (for example, representing the Wilson loop path ordered exponential in terms of a 1d auxiliary fermionic path integral [24][25][26][27][28][29] and integrating out the 4d fields would lead to a non-local 1d fermion action). The AdS 2 multiplet of string fluctuations transverse to the string surface includes [30]: (i) 5 massless scalars y a (S 5 fluctuations near the fixed vacuum point); (ii) 3 massive (m 2 = 2) scalars x i (AdS 5 fluctuations), and (iii) 8 fermions with m 2 = 1.…”

Section: Jhep05(2019)122mentioning

confidence: 99%

“…28 Here we use that for the harmonic functions ( Hi = 0) one has H1H2∂µH3∂µH4 = 1 2 H1H2 (H3H4) → 1 2 (H1H2)H3H4 = ∂µH1∂µH2H3H4 where we dropped a total derivative term. 29 In obtaining the expression (6.54) we included the contributions of diagrams with the − 1 2 n A ζ 2 term in Y A at the points t3 or t4 (like in figure 7 where points x i are now replaced by Y A ). This amounts to a subtraction of contributions at the coinciding points completely analogous to that in (5.9).…”

Section: Jhep05(2019)122mentioning

confidence: 99%

Correlators on non-supersymmetric Wilson line in $$ \mathcal{N}=4 $$ SYM and AdS2/CFT1

Beccaria

Giombi

Tseytlin

2019

101

Correlators of local operators inserted on a straight or circular Wilson loop in a conformal gauge theory have the structure of a one-dimensional "defect" CFT. As was shown in arXiv:1706.00756, in the case of supersymmetric Wilson-Maldacena loop in N = 4 SYM one can compute the leading strong-coupling contributions to 4-point correlators of the simplest "protected" operators by starting with the AdS 5 × S 5 string action expanded near the AdS 2 minimal surface and evaluating the corresponding treelevel AdS 2 Witten diagrams. Here we perform the analogous computations in the nonsupersymmetric case of the standard Wilson loop with no coupling to the scalars. The corresponding non-supersymmetric "defect" CFT 1 should have an unbroken SO(6) global symmetry. The elementary bosonic operators (6 SYM scalars and 3 components of the SYM field strength) are dual respectively to the S 5 embedding coordinates and AdS 5 coordinates transverse to the minimal surface ending on the line at the boundary. The SO(6) symmetry is preserved on the string side provided the 5-sphere coordinates satisfy Neumann boundary conditions (as opposed to Dirichlet in the supersymmetric case); this implies that one should integrate over the S 5 expansion point. The massless S 5 fluctuations then have logarithmic propagator, corresponding to the boundary scalar operator having dimension ∆ = 5 √ λ +. .. at strong coupling. The resulting functions of 1d cross-ratio appearing in the 4-point functions turn out to have a more complicated structure than in the supersymmetric

“…52) where C I (I = 1, 2, 3, 4) are the scalar fields in the bi-fundamental chiral multiplets and M I J is a constant matrix whose diagonalized form is diag(1, 1, −1, −1). The supersymmetric localization allows us to compute the vev of the m multiply-winding Wilson loop W (m) by the matrix model[53] …”

mentioning

confidence: 99%

Towards a C-theorem in defect CFT

Kobayashi

Nishioka

Sato

et al. 2019

102

137

We explore a C-theorem in defect conformal field theories (DCFTs) that unify all the known conjectures and theorems until now. We examine as a candidate C-function the additional contributions from conformal defects to the sphere free energy and the entanglement entropy across a sphere in a number of examples including holographic models. We find the two quantities are equivalent, when suitably regularized, for codimension-one defects (or boundaries), but differ by a universal constant term otherwise. Moreover, we find in a few field theoretic examples that the sphere free energy decreases but the entanglement entropy increases along a certain renormalization group (RG) flow triggered by a defect localized perturbation which is assumed to have a trivial IR fixed point without defects. We hence propose a C-theorem in DCFTs stating that the increment of the regularized sphere free energy due to the defect does not increase under any defect RG flow. We also provide a proof of our proposal in several holographic models of defect RG flows.