S5 Solution Research Articles

New phases of mathcal{N} = 4 SYM at finite chemical potential

We do a systematic search of supergravity solutions that, via the AdS5/CFT4 correspondence, are dual to thermal states in mathcal{N} = 4 SYM at finite chemical potential. These solutions dominate the microcanonical ensemble and are required to ultimately reproduce the microscopic entropy of AdS black holes. Using a mix of analytical and numerical methods, we construct and study static charged hairy solitonic and black hole solutions with global AdS5 asymptotics. They are constructed in two distinct consistent truncations of five dimensional gauged supergravity (and can thus be uplifted to asymptotically AdS5×S5 solutions of type IIB supergravity). In the “single charge” truncation which consists of one charged scalar field, hairy black holes exist above a critical charge and merge with the known Behrndt-Cvetič-Sabra (BCS) black holes along a curve determined by the onset of superradiance in the latter family. The lowest mass hairy black hole is a singular zero entropy soliton. In the “two charge” truncation which consists of a two equal charged scalar fields, hairy black holes exist for all charges and merge with the known BCS black holes along their superradiant onset curve. The lowest mass hairy black hole is a smooth supersymmetric zero entropy soliton. Together with the known phases of the truncation with three equal charges, our findings permit a good understanding of the full phase space of SYM thermal states with three arbitrary chemical potentials.

A new family of AdS4 S-folds in type IIB string theory

We construct infinite new classes of AdS4× S1× S5 solutions of type IIB string theory which have non-trivial SL(2, ℤ) monodromy along the S1 direction. The solutions are supersymmetric and holographically dual, generically, to mathcal{N} = 1 SCFTs in d = 3. The solutions are first constructed as AdS4× ℝ solutions in D = 5 SO(6) gauged supergravity and then uplifted to D = 10. Unlike the known AdS4× ℝ S-fold solutions, there is no continuous symmetry associated with the ℝ direction. The solutions all arise as limiting cases of Janus solutions of d = 4, mathcal{N} = 4 SYM theory which are supported both by a different value of the coupling constant on either side of the interface, as well as by fermion and boson mass deformations. As special cases, the construction recovers three known S-fold constructions, preserving mathcal{N} = 1, 2 and 4 supersymmetry, as well as a recently constructed mathcal{N} = 1 AdS4× S1× S5 solution (not S-folded). We also present some novel “one-sided Janus” solutions that are non-singular.

Holographic Coulomb branch solitons, quasinormal modes, and black holes

Four-dimensional mathcal{N} = 4 supersymmetric Yang-Mills theory, at a point on the Coulomb branch where SU(N) gauge symmetry is spontaneously broken to SU(N − 1) × U(1), admits BPS solitons describing a spherical shell of electric and/or magnetic charges enclosing a region of unbroken gauge symmetry. These solitons have been proposed as gauge theory models for certain features of asymptotically flat extremal black holes. In the ’t Hooft large N limit with large ’t Hooft coupling, these solitons are holographically dual to certain probe D3-branes in the AdS5 × S5 solution of type IIB supergravity. By studying linearised perturbations of these D3-branes, we show that the solitons support quasinormal modes with a spectrum of frequencies sharing both qualitative and quantitative features with asymptotically flat extremal black holes.

Spatially modulated and supersymmetric mass deformations of mathcal{N} = 4 SYM

We study mass deformations of mathcal{N} = 4, d = 4 SYM theory that are spatially modulated in one spatial dimension and preserve some residual supersymmetry. We focus on generalisations of mathcal{N} = 1∗ theories and show that it is also possible, for suitably chosen supersymmetric masses, to preserve d = 3 conformal symmetry associated with a co-dimension one interface. Holographic solutions can be constructed using D = 5 theories of gravity that arise from consistent truncations of SO(6) gauged supergravity and hence type IIB supergravity. For the mass deformations that preserve d = 3 superconformal symmetry we construct a rich set of Janus solutions of mathcal{N} = 4 SYM theory which have the same coupling constant on either side of the interface. Limiting classes of these solutions give rise to RG interface solutions with mathcal{N} = 4 SYM on one side of the interface and the Leigh-Strassler (LS) SCFT on the other, and also to a Janus solution for the LS theory. Another limiting solution is a new supersymmetric AdS4× S1× S5 solution of type IIB supergravity.

Janus on the brane

We present a non-supersymmetric deformation of probe branes describing conformal defects of codimension two in AdS/CFT. The worldvolume of the probe branes is deformed from AdSp× S1 embedded in an AdSp+2× ℳD − p − 2 background to an embedding of Janus form, which uses an AdSp−1 slicing of AdSp and in which the brane bends along the slicing coordinate. In field theory terms this realizes conformal interfaces on codimension- two defects. We discuss these “Janus on the brane” solutions for AdS3× S1 D3-branes in the AdS5× S5 solution of Type IIB, realizing interfaces on surface defects in mathcal{N} = 4 SYM, and show that similar solutions exist for probe branes in AdSp+2× S9−p vacua of M-theory and in the AdS6× S4 solution of massive Type IIA.

Yang-Mills supersymmetry and deformations of AdS5 × S5 solution with the Yang-Baxter equation

The Yang-Mills supersymmetry is considered using the Yang-Baxter equations as deformations of AdS5 × S5 in which they are substituted as a twist of the conformal Drinfeld algebra. The operators here are represented as Killing vectors. The solution of this problem is represented as the Θ-matrix for which the deformation φ was found, which is a super gravitational solution.

Evaluation of vitamin C, nitrate and chlorophyll content determined in lettuce (Thaís, Vanda, Verônica) cultivated in hydroponic system using wastewater

The objective of this work was to determine the levels of vitamin C, nitrate and chlorophyll in three lettuce cultivars in a hydroponic system using waste- and well-water. The experiment was conducted in a hydroponic system using laminar flow technique and nutrients in a protected environment. The experimental design was randomized blocks with treatments set up in split-plots with three replications, whose main plots devoted to lettuce cultivars and sub-plots to hydroponic solutions. The experimental solutions consisted of 7 nutrients (S): S1=Furlani solution, S2=domestic wastewater, S3=optimized domestic wastewater, S4 =well water S5 =optimized well water; S6 = reactor wastewater solution and S7 =optimized reactor wastewater solution and the subplot for the three cultivars of iceberg lettuce (Verônica, Vanda, and Thais). The following variables were determined: nitrate, vitamin C and chlorophyll content using the method described by Lichtenthaler. The results indicated that highest content of vitamin C was found in the Vanda cultivar using the S1 solution. For Veronica cultivar, the highest levels of vitamin C were observed at solutions S1, S2, S3, S4, and S7. The solutions S2 and S3 did not differ from one another in all three cultivars. For the Vanda cultivar, solutions S1, S4 and S7 were the ones that promoted the highest levels of nitrate, 4.61; 3, 32 and 2.64 g kg-1, respectively. Evaluating the effect of the solution within the cultivars, we verified that the highest nitrate values obtained from S2 nutrition for cultivars Thais and Verônica. Regarding the S5 solution, the Verônica cultivar presented the highest concentration of this nutrient. The cultivate Thaís, the highest contents of chlorophyll b were found in solutions S7, S6, S4, S3 and S2, where they did not differ significantly. Regarding to Vanda cultivar the highest values of chlorophyll b were present in solutions S2 and S5. The Verônica cultivar independent of the solution used presented the same values of this pigment.

A type IIB matrix model via non-Abelian T-dualities

We construct a new solution of type IIB supergravity with eight supercharges by applying non-Abelian T-duality to the AdS5 × S5 solution, along the SU(2) isometries in both the internal and Lorentz symmetries. The study of quantised charges and D-brane embeddings suggests a configuration of D1 and D3’-branes that polarise into concentric, spherical, D3 and D5-branes due to the Myers dielectric effect. We find that our solution is dual to a IIB matrix model with fuzzy sphere vacua characterised by partitions of the number of D1 and D3’-branes. We also study the solution obtained via (Abelian) T-dualities along the S1 fiber angles inside the S3’s of the AdS5 × S5 solution. In addition, we point out a precise relation between NATD and ATD solutions by considering a double scaling limit in the NATD solutions. In the particular case of the solutions obtained by a single (non-)Abelian T-duality inside the Lorentz symmetries of the AdS5 × S5 solution, we demonstrate that the double scaling limit provides a supergravity realisation of the relations between the vacua of the half-BPS theories studied by Lin and Maldacena.

Effects of nitrogen form of nutrient solution on uptake and concentration macro element and morphological trait in hydroponic tulip

ABSTRACTEffects of nutrient solution composition ratio on (Tulipa gesneriana L.) cv, ʹApricot Parrotʹ and ʹDaytonaʹ growth and flowering were studied hydroponics. Plants were grown with five treatments respectively: S1(0), S2(0.01), S3(0.02) S4(0.03) and S5(0.04) meq L.-1 ammonium or 0,0.38, 0.74, 0.11 and 0.14 ammonium (NH4+)/NH4+nitrate (NO3)−ratios. Flowering was accelerated by increase of ammonium level for both cultivars. Nutrition solution was not significant on the stem length of Daytona cultivar, but maximum flowering stem length occurred S2 solution for Apricot Parrot cultivar. Increasing ammonium level, decreased potassium concentration in the aerial parts. Total nitrogen of new bulbs decreased with increasing ammonium level for both cultivars. Maximum bulblet production rate occurred in plants that were fed with S5 solution. Maximum flower longevity was in S2 solution for both cultivars. growth and quality of tulip were affected by ammonium level in nutrient solution, so for obtain the best flower quality must added to nutrient solution.

Emergent Lifshitz scaling from N = 4 $$ \mathcal{N}=4 $$ SYM with supersymmetric heavy-quark density

We consider supersymmetric configurations in Type IIB supergravity obtained by the beackreaction of fundamental strings ending on a stack of D3-branes and smeared uniformly in the three spatial directions along the D3-branes. These automatically include a distribution of D5-brane baryon vertices necessary to soak up string charge. The backgrounds are static, preserving eight supersymmetries, an SO(5) global symmetry and symmetry under spatial translations and rotations. We obtain the most general BPS configurations consistent with the symmetries. We show that the solutions to the Type IIB field equations are completely specified by a single function (the dilaton) satisfying a Poisson-like equation in two dimensions. We further find that the equation admits a class of solutions displaying Lifshitz-like scaling with dynamical critical exponent z = 7. The equations also admit an asymptotically AdS5 × S5 solution deformed by the presence of backreacted string sources that yield a uniform density of heavy quarks in $$ \mathcal{N}=4 $$ SYM.

BPS solutions in AdS/CFT

AbstractWe study a class of exact supersymmetric solutions of type IIB Supergravity. They have an SO(4) SU(2) × U(1) isometry and preserve generically 4 of the 32 supersymmetries of the theory. Asymptotically AdS5 × S5 solutions in this class are dual to 1/8 BPS chiral operators which preserve the same symmetries in the 𝒩 = 4 SYM theory. They are parametrized by a set of four functions that satisfy certain differential equations. We analyze the solutions to these equations in a large radius asymptotic expansion: they carry charges with respect to two U(1) KK gauge fields and their mass saturates the expected BPS bound. We show how the same formalism is suitable for the description of excitations of the AdS5 × Yp,q geometries.

Kaluza-Klein holography

We construct a holographic map between asymptotically AdS_5 x S^5 solutions of 10d supergravity and vacuum expectation values of gauge invariant operators of the dual QFT. The ingredients that enter in the construction are (i) gauge invariant variables so that the KK reduction is independent of any choice of gauge fixing; (ii) the non-linear KK reduction map from 10 to 5 dimensions (constructed perturbatively in the number of fields); (iii) application of holographic renormalization. A non-trivial role in the last step is played by extremal couplings. This map allows one to reliably compute vevs of operators dual to any KK fields. As an application we consider a Coulomb branch solution and compute the first two non-trivial vevs, involving operators of dimension 2 and 4, and reproduce the field theory result, in agreement with non-renormalization theorems. This constitutes the first quantitative test of the gravity/gauge theory duality away from the conformal point involving a vev of an operator dual to a KK field (which is not one of the gauged supergravity fields).

Toroidal black holes and T-duality

We consider the toroidal black holes that arise as a generalization of the AdS5×S5 solution of type IIB supergravity. The symmetries of the horizon space allow T-duality transformations that can be exploited to generate new inequivalent black hole solutions of both type IIB and type IIA supergravity, with non-trivial dilaton, B-field, and RR-forms. We examine the asymptotic structure and thermodynamical properties of these solutions.

A non-supersymmetric large N CFT from type 0 string theory

We show that type 0B theory has a classical AdS5 × S5 solution and argue that it is stable at the string-theory level for small enough radius. The dual 4-d conformal field theory is the infrared limit of the theory on N electric D3-branes coincident withN magnetic D3-branes. We explicitly construct this SU(N) × SU(N) gauge theory with global SO(6) symmetry and verify that the one-loop term in the beta function vanishes exactly, while the two-loop term vanishes in the large N limit. We find that this theory is related by a certain projection to the maximally supersymmetric Yang-Mills theory suggesting its largeN conformal invariance to all orders in perturbation theory.