We construct holographic Janus solutions, which describe a conformal interface in the theory of M2-branes, in four-dimensional gauged supergravities using a perturbative method. In particular, we study three Einstein-scalar systems and their BPS equations, which are derived by Bobev, Pilch, and Warner (2014). The actions of our interest are all consistent truncations of $D=11$ supergravity chosen to be invariant under $SO(4)\times SO(4)$, $SU(3)\times U(1)\times U(1)$, and $G_2$ symmetry subgroups of $SO(8)$ respectively. The utility of our semi-analytic result is illustrated by the calculation of minimal area surface and the associated holographic entanglement entropy.
We investigate the various properties Janus supersymmetric Yang-Mills theories. A novel vacuum structure is found and BPS monopoles and dyons are studied. Less supersymmetric Janus theories found before are derived by a simpler method. In addition, we find the supersymmetric theories when the coupling constant depends on two and three spatial coordinates.
We study supersymmetric Janus solutions of dyonic $ISO(7)$-gauged $\mathcal{N}$ = 8 supergravity. We mostly find Janus solutions flowing to 3d $\mathcal{N}$ = 8 SYM phase which is the worldvolume theory on D2-branes and non-conformal. There are also solutions flowing from the critical points which are dual to 3d SCFTs from deformations of the D2-brane theory.
We explore the physics of supersymmetric Janus gauge theories in four dimension with spatial dependent coupling constants, e^2 and theta. For the 8 supersymmetric case, we study the vacuum and BPS spectrum, and the physics of a sharp interface where the couple constants jump. We also find less supersymmetric cases either due to additional expressions in the Lagrangian or to the fact that coupling constants depend on additional spatial coordinates.
We construct supersymmetric Janus solutions using four-dimensional $N=3$ gauged supergravity with $SO(3)\times SU(3)$ gauge group. The $N=3$ supersymmetric $AdS_4$ vacuum with unbroken $SO(3)\times SU(3)$, identified with the compactification of eleven-dimensional supergravity on $AdS_4\times N^{010}$, provides a gravity dual of supersymmetric $N=3$ Chern-Simons-Matter theory in three dimensions with $SU(3)$ flavor symmetry. The Janus solutions accordingly describe supersymmetric conformal interfaces within this Chern-Simons-Matter theory via the AdS/CFT holography. We find two classes of Janu…
We compute holographic complexity for the non-supersymmetric Janus deformation of AdS$_5$ according to the volume conjecture. The result is characterized by a power-law ultraviolet divergence. When a ball-shaped region located around the interface is considered, a sub-leading logarithmic divergent term and a finite part appear in the corresponding subregion volume complexity. Using two different prescriptions to regularize the divergences, we find that the coefficient of the logarithmic term is universal.
We study the Janus interface, a domain wall characterized by spatially varying couplings, in two-dimensional N=(2,2) supersymmetric gauge theories on the two-sphere. When the variations of the couplings are small enough, SUSY localization in the Janus background gives an analytic continuation of the sphere partition function. This directly demonstrates that the interface entropy is proportional to the quantity known as Calabi's diastasis, as originally shown by Bachas et al. When the variations are not small, we propose that an analytic continuation of the sphere partition function coincides w…
We explicitly truncate N = 8 gauged supergravity in five dimensions to its SU(3)-invariant sector with dilaton and axion fields. We show that this truncation has a solution which is identical to the super Janus constructed in N = 2 gauged supergravity in five dimensions. Then we lift the solution of the SU(3)-invariant truncation to type IIB supergravity by employing the consistent truncation ansatz. We show that the lifted solution falls into a special case of the supersymmetric Janus solutions constructed in type IIB supergravity. Additionally, we also prove that the lifted solution provides…
The reduced field equations and BPS conditions are derived in Type IIB supergravity for configurations of the Janus type, characterized by an $AdS_4$-slicing of $AdS_5$, and various degrees of internal symmetry and supersymmetry. A generalization of the Janus solution, which includes a varying axion along with a varying dilaton, and has SO(6) internal symmetry, but completely broken supersymmetry, is obtained analytically in terms of elliptic functions. A supersymmetric solution with 4 conformal supersymmetries, SU(3) internal symmetry, a varying axion along with a varying dilaton, and non-tri…
We give a large class of supersymmetric Janus solutions in $ω$-deformed (dyonic) $SO(8)$ maximal gauged supergravity with $ω=\fracπ{8}$. Unlike the purely electric counterpart, the dyonic $SO(8)$ gauged supergravity exhibits a richer structure of $AdS_4$ vacua with $N=8,2,1,1$ supersymmetries and $SO(8)$, $U(3)$, $G_2$ and $SU(3)$ symmetries, respectively. Similarly, domain walls interpolating among these critical points show a very rich structure as well. In this paper, we show that this gauged supergravity also accommodates a number of interesting supersymmetric Janus solutions in the form o…
The complete Type IIB supergravity solutions with 16 supersymmetries are obtained on the manifold $AdS_4 \times S^2 \times S^2 \times Σ$ with $SO(2,3) \times SO(3) \times SO(3)$ symmetry in terms of two holomorphic functions on a Riemann surface $Σ$, which generally has a boundary. This is achieved by reducing the BPS equations using the above symmetry requirements, proving that all solutions of the BPS equations solve the full Type IIB supergravity field equations, mapping the BPS equations onto a new integrable system akin to the Liouville and Sine-Gordon theories, and mapping this integrabl…
We use maximal gauged supergravity in four dimensions to construct the gravity dual of a class of supersymmetric conformal interfaces in the theory on the world-volume of multiple M2-branes. We study three classes of examples in which the $(1+1)$-dimensional defects preserve $(4,4)$, $(0,2)$ or $(0,1)$ supersymmetry. Many of the solutions have the maximally supersymmetric $AdS_4$ vacuum dual to the $\mathcal{N}=8$ ABJM theory on both sides of the interface. We also find new special classes of solutions including one that interpolates between the maximally supersymmetric vacuum and a conformal …
We study $N=4$ gauged supergravity with $SO(4)\times SO(4)$ gauge group in the presence of symplectic deformations and find new classes of Janus solutions preserving $N=1$ and $N=2$ supersymmetries. The $N=2$ solutions preserve $SO(2)\times SO(2)\times SO(2)\times SO(2)$ symmetry and interpolate between $N=4$ supersymmetric $AdS_4$ vacua with $SO(4)\times SO(4)$ symmetry. These correspond holographically to $N=(2,0)$ two-dimensional conformal defects within the dual $N=4$ CSM theories with $SO(4)\times SO(4)$ symmetry. The $N=1$ solutions contain two families of Janus configurations, one inter…
In this paper we compute the holographic boundary entropy for half-BPS Janus deformations of the $AdS_3\times S^3\times T^4$ vacuum of type IIB supergravity. Previous work \cite{Chiodaroli:2009yw} has shown that there are two independent deformations of this sort. In one case, the six-dimensional dilaton jumps across the interface, while the other case displays a jump of axion and four-form potential. In case of a jump of the six-dimensional dilaton, it is possible to compare the holographic result with the weak-coupling result for a two-dimensional interface CFT where the radii of the compact…
We investigate a family of SU(3)$\times$U(1)$\times$U(1)-invariant holographic flows and Janus solutions obtained from gauged $\mathcal{N}=8$ supergravity in four dimensions. We give complete details of how to use the uplift formulae to obtain the corresponding solutions in M theory. While the flow solutions appear to be singular from the four-dimensional perspective, we find that the eleven-dimensional solutions are much better behaved and give rise to interesting new classes of compactification geometries that are smooth, up to orbifolds, in the infra-red limit. Our solutions involve new pha…
We propose and study a supersymmetric version of the Janus domain wall solution of type IIB supergravity. Janus is dual to N=4 super Yang Mills theory with a coupling constant that jumps across an interface. While the interface in the Janus field theory completely breaks all supersymmetries, it was found earlier that some supersymmetry can be restored in the field theory at the cost of breaking the SO(6) R-symmetry down to at least SU(3). We find the gravity dual to this supersymmetric interface theory by studying the SU(3) invariant subsector of N=8 gauged supergravity in 5D, which is describ…
The S-fold description of Janus-type solutions of type IIB supergravity is investigated. This is done by first studying a $\,\textrm{U}(1) \times \textrm{U}(1)\,$ invariant sector of the four-dimensional dyonically-gauged $\,{[\,\textrm{SO}(1,1) \times \textrm{SO}(6)\,] \ltimes \mathbb{R}^{12}}\,$ maximal supergravity that arises upon reduction of type IIB supergravity on $\,\mathbb{R} \, \times \, \textrm{S}^{5}\,$. Two AdS$_{4}$ solutions preserving $\,\textrm{SU}(3)\,$ and $\,\textrm{SO}(6)\,$ gauge symmetry together with $\,\mathcal{N}=1\,$ and $\,\mathcal{N}=0\,$ supersymmetry are found w…
We study holographic RG flow solutions within four-dimensional $N=4$ gauged supergravity obtained from type IIA and IIB string theories compactified on $T^6/\mathbb{Z}_2\times \mathbb{Z}_2$ orbifold with gauge, geometric and non-geometric fluxes. In type IIB non-geometric compactifications, the resulting gauged supergravity has $ISO(3)\times ISO(3)$ gauge group and admits an $N=4$ $AdS_4$ vacuum dual to an $N=4$ superconformal field theory (SCFT) in three dimensions. We study various supersymmetric RG flows from this $N=4$ SCFT to $N=4$ and $N=1$ non-conformal field theories in the IR. The flo…
We found a simple and interesting generalization of the non-supersymmetric Janus solution in type IIB string theory. The Janus solution can be thought of as a thick AdS_d-sliced domain wall in AdS_{d+1} space. It turns out that the AdS_d-sliced domain wall can support its own AdS_{d-1}-sliced domain wall within it. Indeed this pattern persists further until it reaches the AdS_2-slice of the domain wall within self-similar AdS_{p (2<p\le d)}-sliced domain walls. In other words the solution represents a sequence of little Janus nested in the interface of the parent Janus according to a remarkabl…
We give a large class of new supersymmetric Janus solutions in dyonic $ISO(7)$ maximal gauged supergravity encompassing all known solutions appearing recently. We consider $SO(3)$ invariant sector in which the gauged supergravity admits four supersymmetric $AdS_4$ vacua with $N=1,1,2,3$ unbroken supersymmetries and $G_2$, $SU(3)$, $SU(3)\times U(1)$ and $SO(4)$ symmetries, respectively. We find Janus solutions preserving $N=1,2,3$ supersymmetries and interpolating between $AdS_4$ vacua and the $N=8$ SYM phase. These solutions can be interpreted as conformal interfaces between SYM and various c…
Based on the recent proposal of N=8 superconformal gauge theories of the multiple M2 branes, we derive (2+1)-dimensional supersymmetric Janus field theories with a space-time dependent coupling constant. From the original Bagger-Lambert model, we get a supersymmetric field theory with a similar action to the N D2 branes, but the coupling varies with the space-time as a function of the light-cone coordinate, g(t+x). Half of the supersymmetries can be preserved. We further investigate the M2 brane action deformed by mass and Myers-like terms. In this case, the final YM action is deformed by mass…
This paper investigates scalar perturbations in the top-down supersymmetric Janus solutions dual to conformal interfaces in the $D1/D5$ CFT, finding analytic closed-form solutions. We obtain an explicit representation of the bulk-to-bulk propagator and extract the two-point correlation function of the dual operator with itself, whose form is not fixed by symmetry alone. We give an expression involving the sum of conformal blocks associated with the bulk-defect operator product expansion and briefly discuss finite-temperature extensions. To our knowledge, this is the first two-point function co…
We study an $SO(2)\times SO(2)\times SO(2)\times SO(2)$ truncation of four-dimensional $N=4$ gauged supergravity coupled to six vector multiplets with $SO(4)\times SO(4)$ gauge group and find a new class of holographic RG flows and supersymmetric Janus solutions. In this truncation, there is a unique $N=4$ supersymmetric $AdS_4$ vacuum dual to an $N=4$ SCFT in three dimensions. In the presence of the axion, the RG flows generally preserve $N=2$ supersymmetry while the supersymmetry is enhanced to $N=4$ for vanishing axion. We find solutions interpolating between the $AdS_4$ vacuum and singular…
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 $AdS_{p}\times S^1$ embedded in an $AdS_{p+2} \times \mathcal M^{D-p-2}$ background to an embedding of Janus form, which uses an $AdS_{p-1}$ slicing of $AdS_p$ 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 $AdS_3\times S^1$ D3-branes in the $AdS_5\times S^5$ solution of Type I…
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 $d=3$…
We show that for every Sasaki-Einstein manifold, $M_5$, the AdS$_5\times M_5$ background of type IIB supergravity admits two universal deformations leading to supersymmetric AdS$_4$ solutions. One class of solutions describes an AdS$_4$ domain wall in AdS$_5$ and is dual to a Janus configuration with $\mathcal{N}=1$ supersymmetry. The other class of backgrounds is of the form AdS$_4\times S^1\times M_5$ with a non-trivial SL$(2,\mathbb{Z})$ monodromy for the IIB axio-dilaton along the $S^1$. These AdS$_4$ solutions are dual to three-dimensional $\mathcal{N}=1$ SCFTs. Using holography we expres…
Motivated by an analysis of the sub-superalgebras of the five-dimensional superconformal algebra $F(4)$, we search for the holographic duals to co-dimension one superconformal defects in 5d CFTs which have $SO(4,2) \oplus U(1)$ bosonic symmetry. In particular, we look for domain wall solutions to six-dimensional $F(4)$ gauged supergravity coupled to a single vector multiplet. It is found that supersymmetric domain wall solutions do not exist unless there is a non-trivial profile for one of the vector multiplet scalars which is charged under the gauged $SU(2)$ R-symmetry. This non-trivial profi…
In this note, we describe supersymmetric backgrounds for the four-dimensional maximally supersymmetric Yang-Mills theory. As an extension of the method of Festuccia and Seiberg to sixteen supercharges in four dimensions, we utilize the coupling of the gauge theory to maximally extended conformal supergravity. Included among the fields of the conformal supergravity multiplet is the complexified coupling parameter of the gauge theory; therefore, backgrounds with spacetime varying coupling--such as appear in F-theory and Janus configurations--are naturally included in this formalism. We demonstra…
We construct supersymmetric solutions of $D=11$ supergravity, preserving 1/4 of the supersymmetry, that are holographically dual to ABJM theory which has been deformed by spatially varying mass terms depending on one of the two spatial directions. We show that the BPS equations reduce to the Helmholtz equation on the complex plane leading to rich classes of new solutions. In particular, the construction gives rise to infinite classes of supersymmetric boomerang RG flows, as well as generalising a known Janus solution.
We propose and study a specific gauge theory dual of the smooth, non-supersymmetric (and apparently stable) Janus solution of Type IIB supergravity found in hep-th/0304129. The dual field theory is N=4 SYM theory on two half-spaces separated by a planar interface with different coupling constants in each half-space. We assume that the position dependent coupling multiplies the operator L' which is the fourth descendent of the primary Tr(X^I X^J) and closely related to the N=4 Lagrangian density. At the classical level supersymmetry is broken explicitly, but SO(3,2) conformal symmetry is preser…
We study the supersymmetric partition function of a 2d linear $σ$-model whose target space is a torus with a complex structure that varies along one worldsheet direction and a Kähler modulus that varies along the other. This setup is inspired by the dimensional reduction of a Janus configuration of 4d $\mathcal{N}=4$ $U(1)$ Super-Yang-Mills theory compactified on a mapping torus ($T^2$ fibered over $S^1$) times a circle with an $SL(2,\mathbb{Z})$ duality wall inserted on $S^1$, but our setup has minimal supersymmetry. The partition function depends on two independent elements of $SL(2,\mathbb{…
We study deformations of ${\cal N}=4$ supersymmetric Yang-Mills theory with couplings and masses depending on space-time. The conditions to preserve part of the supersymmetry are derived and a lot of solutions of these conditions are found. The main example is the case with $ISO(1,1)\times SO(3)\times SO(3)$ symmetry, in which couplings, as well as masses and the theta parameter, can depend on two spatial coordinates. In the case $ISO(1,1)$ is enhanced to $ISO(1,2)$, it reproduces the supersymmetric Janus configuration found by Gaiotto and Witten. When $SO(3)\times SO(3)$ is enhanced to $SO(6)…
In this note we calculate the holographic entanglement entropy in the presence of a conformal interface for a geometric configuration in which the entangling region ${\cal A}$ lies on one side of the interface. For the supersymmetric Janus solution we find exact agreement between the holographic and CFT calculation of the entanglement entropy.
We study deformations of ${\cal N}=4$ supersymmetric Yang-Mills theory with space-time dependent couplings by embedding probe D3-branes in supergravity backgrounds with non-trivial fluxes. The effective action on the world-volume of the D3-branes is analyzed and a map between the deformation parameters and the fluxes is obtained. As an explicit example, we consider D3-branes in a background corresponding to $(p,q)$ 5-branes intersecting them and show that the effective theory on the D3-branes precisely agrees with the supersymmetric Janus configuration found by Gaiotto and Witten in arXiv:0804…
Type IIB superstring theory has AdS_3 x S^3 x M_4 (where the manifold M_4 is either K_3 or T^4) solutions which preserve sixteen supersymmetries. In this paper we consider half-BPS solutions which are locally asymptotic to AdS_3 x S^3 x M_4 and preserve eight of the sixteen supersymmetries. We reduce the BPS equations and the Bianchi identity for the self-dual five-form field to a set of four differential equations. The complete local solution can be parameterized in terms of two harmonic and two holomorphic functions and all bosonic fields have explicit expressions in terms of these functions…
We study supersymmetric solutions in four-dimensional $N=6$ gauged supergravity with $SO(6)$ gauge group. There is a unique $N=6$ supersymmetric $AdS_4$ vacuum with $SO(6)$ symmetry dual to an $N=6$ SCFT in three dimensions. We find a number of domain walls interpolating between this $AdS_4$ vacuum and singular geometries in the IR with $SO(2)\times SO(4)$, $U(3)$, $SO(3)$ and $SO(2)\times SO(2)\times SO(2)$ symmetries. The $SO(3)$ case admits $N=6$ or $N=2$ solutions depending on whether the pseudoscalars are present or not. On the other hand, all the remaining solutions preserve $N=6$ supers…
We study a large class of supersymmetric solutions in four-dimensional $N=5$ gauged supergravity with $SO(5)$ gauge group. There is only one $N=5$ supersymmetric $AdS_4$ vacuum preserving the full $SO(5)$ symmetry dual to an $N=5$ SCFT in three dimensions. We give a number of domain walls interpolating between this $AdS_4$ fixed point and singular geometries in the IR with $SO(4)$ and $SO(3)$ symmetries. These solutions describe RG flows from the $N=5$ SCFT to non-conformal field theories driven by mass deformations. The $SO(4)$ solutions are precisely in agreement with the previously known ma…
We construct infinite new classes of $AdS_4\times S^1\times S^5$ solutions of type IIB string theory which have non-trivial $SL(2,\mathbb{Z})$ monodromy along the $S^1$ direction. The solutions are supersymmetric and holographically dual, generically, to $\mathcal{N}=1$ SCFTs in $d=3$. The solutions are first constructed as $AdS_4\times \mathbb{R}$ solutions in $D=5$ $SO(6)$ gauged supergravity and then uplifted to $D=10$. Unlike the known $AdS_4\times \mathbb{R}$ S-fold solutions, there is no continuous symmetry associated with the $\mathbb{R}$ direction. The solutions all arise as limiting c…
We study Wilson loops in string theory realizations of AdS/BCFT and wedge holography. The field theories are based on 3d $\mathcal N=4$ long quiver gauge theories engineered by D3, D5 and NS5 branes, and on BCFTs involving 4d $\mathcal N=4$ SYM coupled to such 3d theories. The holographic duals have geometry $AdS_4\times S^2\times S^2$ warped over a strip. We identify the holographic representation of antisymmetric Wilson loops associated with individual 3d gauge nodes in terms of probe D5-branes. The expectation values obtained holographically are matched to supersymmetric localization comput…
We derive a formula for the half-BPS interface entropy between any pair of ${\cal N}=(4,4)$ theories on the same conformal manifold. This generalizes the diastasis formula derived in arXiv:1311.2202 for ${\cal N}=(2,2)$ theories, which is restricted to the conformal submanifolds generated by either chiral or twisted chiral multiples of ${\cal N}=(2,2)$ supersymmetry. To derive the ${\cal N}=(4,4)$ formula, we use the fact that the conformal manifold of ${\cal N}=(4,4)$ theories is symmetric and quaternionic-Kähler and that its isotropy group contains the $SU(2) \otimes SU(2)$ external automorp…
