Supersymmetric Wilson loops at two loops

We study the quantum properties of certain BPS Wilson loops in ${\cal N}=4$ supersymmetric Yang-Mills theory. They belong to a general family, introduced recently, in which the addition of particular scalar couplings endows generic loops on $S^3$ with a fraction of supersymmetry. When restricted to $S^2$, their quantum average has been further conjectured to be exactly computed by the matrix model governing the zero-instanton sector of YM$_2$ on the sphere. We perform a complete two-loop analysis on a class of cusped Wilson loops lying on a two-dimensional sphere, finding perfect agreement with the conjecture. The perturbative computation reproduces the matrix-model expectation through a highly non-trivial interplay between ladder diagrams and self-energies/vertex contributions, suggesting the existence of a localization procedure.Comment: 35 pages, 14 figures, typos corrected, references adde

Two-dimensional non-commutative Yang-Mills theory: coherent effects in open Wilson line correlators

A perturbative calculation of the correlator of three parallel open Wilson lines is performed for the U(N) theory in two non-commutative space-time dimensions. In the large-N planar limit, the perturbative series is fully resummed and asymptotically leads to an exponential increase of the correlator with the lengths of the lines, in spite of an interference effect between lines with the same orientation. This result generalizes a similar increase occurring in the two-line correlator and is likely to persist when more lines are considered provided they share the same direction.Comment: 22 pages, 1 figure, typeset in JHEP styl

Correlators of supersymmetric Wilson-loops, protected operators and matrix models in N=4 SYM

We study the correlators of a recently discovered family of BPS Wilson loops in ${\cal N}=4$ supersymmetric U(N) Yang-Mills theory. When the contours lie on a two-sphere in the space-time, we propose a closed expression that is valid for all values of the coupling constant $g$ and for any rank $N$, by exploiting the suspected relation with two-dimensional gauge theories. We check this formula perturbatively at order ${\cal O}(g^4)$ for two latitude Wilson loops and we show that, in the limit where one of the loops shrinks to a point, logarithmic corrections in the shrinking radius are absent at ${\cal O}(g^6)$. This last result strongly supports the validity of our general expression and suggests the existence of a peculiar protected local operator arising in the OPE of the Wilson loop. At strong coupling we compare our result to the string dual of the ${\cal N}=4$ SYM correlator in the limit of large separation, presenting some preliminary evidence for the agreement.Comment: 20 page, 8 figure

Wilson line correlators in two-dimensional noncommutative Yang-Mills theory

We study the correlator of two parallel Wilson lines in two-dimensional noncommutative Yang-Mills theory, following two different approaches. We first consider a perturbative expansion in the large-N limit and resum all planar diagrams. The second approach is non-perturbative: we exploit the Morita equivalence, mapping the two open lines on the noncommutative torus (which eventually gets decompacted) in two closed Wilson loops winding around the dual commutative torus. Planarity allows us to single out a suitable region of the variables involved, where a saddle-point approximation of the general Morita expression for the correlator can be performed. In this region the correlator nicely compares with the perturbative result, exhibiting an exponential increase with respect to the momentum p.Comment: 21 pages, 1 figure, typeset in JHEP style; some formulas corrected in Sect.3, one reference added, results unchange

On the invariance under area preserving diffeomorphisms of noncommutative Yang-Mills theory in two dimensions

We present an investigation on the invariance properties of noncommutative Yang-Mills theory in two dimensions under area preserving diffeomorphisms. Stimulated by recent remarks by Ambjorn, Dubin and Makeenko who found a breaking of such an invariance, we confirm both on a fairly general ground and by means of perturbative analytical and numerical calculations that indeed invariance under area preserving diffeomorphisms is lost. However a remnant survives, namely invariance under linear unimodular tranformations.Comment: LaTeX JHEP style, 16 pages, 2 figure

Area-preserving diffeomorphisms in gauge theory on a non-commutative plane: a lattice study

We consider Yang-Mills theory with the U(1) gauge group on a non-commutative plane. Perturbatively it was observed that the invariance of this theory under area-preserving diffeomorphisms (APDs) breaks down to a rigid subgroup SL(2,R). Here we present explicit results for the APD symmetry breaking at finite gauge coupling and finite non-commutativity. They are based on lattice simulations and measurements of Wilson loops with the same area but with a variety of different shapes. Our results are consistent with the expected loss of invariance under APDs. Moreover, they strongly suggest that non-perturbatively the SL(2,R) symmetry does not persist either.Comment: 28 pages, 15 figures, published versio

Therapeutically targeting guanylate cyclase-C: computational modeling of plecanatide, a uroguanylin analog

Plecanatide is a recently developed guanylate cyclase‐C (GC‐C) agonist and the first uroguanylin analog designed to treat chronic idiopathic constipation (CIC) and irritable bowel syndrome with constipation (IBS‐C). GC‐C receptors are found across the length of the intestines and are thought to play a key role in fluid regulation and electrolyte balance. Ligands of the GC‐C receptor include endogenous agonists, uroguanylin and guanylin, as well as diarrheagenic, Escherichia coli heat‐stable enterotoxins (ST). Plecanatide mimics uroguanylin in its 2 disulfide‐bond structure and in its ability to activate GC‐Cs in a pH‐dependent manner, a feature associated with the presence of acid‐sensing residues (Asp2 and Glu3). Linaclotide, a synthetic analog of STh (a 19 amino acid member of ST family), contains the enterotoxin's key structural elements, including the presence of three disulfide bonds. Linaclotide, like STh, activates GC‐Cs in a pH‐independent manner due to the absence of pH‐sensing residues. In this study, molecular dynamics simulations compared the stability of plecanatide and linaclotide to STh. Three‐dimensional structures of plecanatide at various protonation states (pH 2.0, 5.0, and 7.0) were simulated with GROMACS software. Deviations from ideal binding conformations were quantified using root mean square deviation values. Simulations of linaclotide revealed a rigid conformer most similar to STh. Plecanatide simulations retained the flexible, pH‐dependent structure of uroguanylin. The most active conformers of plecanatide were found at pH 5.0, which is the pH found in the proximal small intestine. GC‐C receptor activation in this region would stimulate intraluminal fluid secretion, potentially relieving symptoms associated with CIC and IBS‐C

Therapeutically targeting guanylate cyclase-C: computational modeling of plecanatide, a uroguanylin analog

Plecanatide is a recently developed guanylate cyclase‐C (GC‐C) agonist and the first uroguanylin analog designed to treat chronic idiopathic constipation (CIC) and irritable bowel syndrome with constipation (IBS‐C). GC‐C receptors are found across the length of the intestines and are thought to play a key role in fluid regulation and electrolyte balance. Ligands of the GC‐C receptor include endogenous agonists, uroguanylin and guanylin, as well as diarrheagenic, Escherichia coli heat‐stable enterotoxins (ST). Plecanatide mimics uroguanylin in its 2 disulfide‐bond structure and in its ability to activate GC‐Cs in a pH‐dependent manner, a feature associated with the presence of acid‐sensing residues (Asp2 and Glu3). Linaclotide, a synthetic analog of STh (a 19 amino acid member of ST family), contains the enterotoxin's key structural elements, including the presence of three disulfide bonds. Linaclotide, like STh, activates GC‐Cs in a pH‐independent manner due to the absence of pH‐sensing residues. In this study, molecular dynamics simulations compared the stability of plecanatide and linaclotide to STh. Three‐dimensional structures of plecanatide at various protonation states (pH 2.0, 5.0, and 7.0) were simulated with GROMACS software. Deviations from ideal binding conformations were quantified using root mean square deviation values. Simulations of linaclotide revealed a rigid conformer most similar to STh. Plecanatide simulations retained the flexible, pH‐dependent structure of uroguanylin. The most active conformers of plecanatide were found at pH 5.0, which is the pH found in the proximal small intestine. GC‐C receptor activation in this region would stimulate intraluminal fluid secretion, potentially relieving symptoms associated with CIC and IBS‐C