Interface Yang-Mills, Supersymmetry, and Janus

Eric D'Hoker; John Estes; Michael Gutperle

REVIEW

Interface Yang-Mills, Supersymmetry, and Janus

Eric D'Hoker, John Estes, Michael Gutperle

High Energy Physics - Theory · Submitted 2 Mar 2006 · 26 references

Pith's verdict: A serious classification paper with two new explicit interface Lagrangians, but the load-bearing reduction to the seven algebraic equations is asserted rather than shown; the 16/8/4 uniqueness claim is conditional on that algebra.

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arXiv IDhep-th/0603013 (version 1)

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CitationEric D'Hoker, John Estes, Michael Gutperle. "Interface Yang-Mills, Supersymmetry, and Janus." arXiv:hep-th/0603013 (2006). https://pith.science/paper/MCVADD2O

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Editor's note

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Here's the short version: this paper deserves referee time. It poses a clean Lagrangian-level question—what supersymmetry can an interface in N=4 SYM preserve if the interface carries no degrees of freedom and only local gauge-invariant operators of dimension at most 3 are allowed—and it answers with a systematic algebraic classification. The genuinely new output is in Section 5: two explicit interface Lagrangians with 8 and 4 Poincaré supercharges, enhanced to 16 and 8 conformal supercharges, with SU(2)xSU(2) and SO(2)xSU(2) R-symmetry. The earlier SU(3) Janus theory falls out as the r=1 case. That is a substantive addition to the Janus and defect-CFT literature, and the paper is well organized about what it has and has not shown.

The soft spot is exactly what the stress-test note says. The step from 'vary the full action' to the seven equations (3.15) is not shown. Section 3.1 states that the variations of L_I are straightforward but lengthy and will not be presented. For a classification whose headline is 'exactly these three families', that omission is load-bearing. The claims about independent monomials and the Clifford linear-independence are plausible—I checked the structure, not every line—but they are asserted. A sign error or a missed total derivative there propagates directly into the completeness of the 16/8/4 list. A second, smaller conditionality: z_4 is fixed in Section 4 by choosing (3.22) rather than derived as the unique solution, so the conformal-limit analysis in Section 6 inherits that choice. On the other hand, the reader's circularity concern does not land: the derivation starts from standard N=4 SYM and recovers [11] as a special case; nothing is fitted to a target result. And Section 7's own admission—the D3-D5 symmetries match but the multiplet content differs, so a decoupling mechanism would be needed—is handled honestly. That weakens the holographic identification of the maximal theory, not the field-theory classification itself.

Bottom line: if I were the editor, I would send this to a referee willing to do or at least spot-check the omitted variation computation. It should not be desk-rejected. The paper is for people working on defect holography and supersymmetric Janus; readers who want the result without redoing the algebra should treat the 16/8/4 uniqueness as conditional until the derivation of (3.15) is available or independently verified.

Referee report

Major objections (3)

[Section 3.1] The reduction of the supersymmetry variation condition (3.9) to the coefficient equations (3.10)-(3.14), and the subsequent reduction to the seven equations (3.15), is not shown. The text states that the variations δ0L_I, δI L_0, and δI L_I are 'straightforward, but the resulting expressions are lengthy and will not be presented here.' These equations are the foundation of the entire classification: any error in the omitted computation—an unaccounted total derivative, a missing monomial, or a mistaken Clifford identity—propagates to the solution in Section 4 and the classification in Section 5. The authors should include the full computation in an appendix, or at least provide the list of independent field monomials, the resulting expressions, and the γ-matrix identities used to reduce (3.12) and (3.13) to equations (1)-(2) and (4)-(5).
[Section 3.4] Equation (7') is not solved in the text; the paper states that a nonzero ξ 'allows for a simple solution' (3.22) and that this value 'can be taken' for z4. Since z4 does not appear in the remaining equations, this would be a restriction on the space of interface couplings unless it is the unique solution. In fact, the unique real solution of (7') is (3.22), because the map v^j ↦ v^j (ρ_j)^* ξ^* from R^6 to the spinor space is injective for any nonzero ξ. The manuscript, however, does not give this argument; it should be added, since the conformal-limit analysis of Section 6 relies on (3.22) to derive (6.5) and (6.6).
[Section 3.1, eq. (3.7)] The modified supersymmetry transformation is assumed to take the form δIψ=(∂πg)χ_i φ_i with δI Aμ=δI φ_i=0. The completeness of the classification depends on this being the most general form compatible with chirality, engineering dimension, and 2+1-dimensional Poincaré invariance. The authors should justify exhaustiveness, in particular why terms such as (∂πg) γ^π χ_i φ_i are excluded by the chirality of δψ.

Minor objections (4)

[Section 6, eq. (6.3)] The off-diagonal conditions (i≠j) in (6.3) are not discussed; after computing the exponents n_i from the diagonal equations, the authors should explicitly verify that the off-diagonal conditions are satisfied by the supersymmetry solution, as they are for the explicit Lagrangians in Section 5.
[Abstract] The abstract contains a typo: 'constructe d' should read 'constructed'.
[Section 3.4] The sentence 'For every ξ satisfying these equations, we will have two real supersymmetries given by ξ+ and ξ−' would benefit from a brief clarification of how the counting of real supercharges per complex solution works, since the later sections use numbers like 2, 4, and 8.
[Section 5.1, eq. (5.4)] In the condition b = c e^{i4θ} with b,c ≥ 0, the paper should explicitly state that this forces either b=c=0 or b=c with e^{i4θ}=1; this is the basis for the three cases in (5.5).

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The paper

The paper claims

The paper classifies all supersymmetric planar interfaces of N=4 super-Yang-Mills with varying gauge coupling, finding exactly three families.

The reading

This paper asks which supersymmetries can survive when $N=4$ super-Yang-Mills lives on both sides of a planar interface and the gauge coupling varies across it. The authors show that demanding supersymmetry of the full interface action reduces to seven algebraic equations, and that solving those equations completely leaves exactly three families with maximal internal symmetry: one with 8 Poincaré supercharges (enhanced to 16 conformal supercharges) and $SU(2)\times SU(2)$ R-symmetry, one with 4 Poincaré supercharges (enhanced to 8) and $SO(2)\times SU(2)$ R-symmetry, and the previously proposed $SU(3)$ theory with 2 Poincaré supercharges (enhanced to 4). The Lagrangians for all three are written out explicitly, and the conformal limit is shown to exist when the $(\partial_\pi g)^2$ term can be removed by rescaling scalar fields. If the classification is correct, any future supersymmetric interface CFT of this type must be one of these theories, which sharpens the search for their gravity duals.

What carries the argument

The load-bearing mechanism is the reduction of interface supersymmetry to seven algebraic equations (eq. (3.15), recast as (3.21)). The variables are the interface couplings $y_1$, $Y_2$, $Y_3$, $z^1_{ij}$, $z^2_{ij}$, $z^3_{ijk}$, $z^4_{ij}$ and the supersymmetry spinor $\zeta$; $Y_3$ is the complex symmetric matrix of trilinear fermionic interface couplings. The equations are solved by choosing $SU(4)$ gauge so that $Y_2=0$, by using Lemma 1 to diagonalize the complex symmetric matrix $Y_3=U D_3 U^t e^{i\theta_0}$ with $D_3$ real, non-negative, diagonal, and by working in the basis where the supersymmetry spinor points along an eigenvector of $D_3$. The number of unit eigenvalues of $D_3$, equivalently the rank of $Y_3^\dagger Y_3$, then determines how many supercharges survive, with the Clifford-algebra identities of the $\rho_i$ matrices converting the spinor constraints into purely algebraic ones.

Extended reading notes

Core claim

The central claim is a systematic, complete classification of interface supersymmetry for $N=4$ super-Yang-Mills on either side of a planar interface, with a smoothly varying gauge coupling $g(x^\pi)$, no independent interface degrees of freedom, and interface couplings restricted to local gauge-invariant operators of dimension at most three built from $\partial_\pi g$. The paper reduces the supersymmetry conditions to seven algebraic equations and solves them in closed form, up to $SU(4)$ rotations. The solutions give: $\mathcal{N}=4$ interface supersymmetry with 8 real Poincaré supercharges, $SU(2)\times SU(2)$ R-symmetry, and 16 conformal supercharges; $\mathcal{N}=2$ interface supersymmetry with 4 real Poincaré supercharges, $SO(2)\times SU(2)$ R-symmetry, and 8 conformal supercharges; and the earlier $\mathcal{N}=1$ interface theory with 2 real Poincaré supercharges, $SU(3)$ internal symmetry, and 4 conformal supercharges. Explicit Lagrangians are constructed in Section 5, and the existence of the conformal limit is tied to removing the $(\partial_\pi g)^2$ term by field rescaling. The paper also notes that the maximal-symmetry theory has precisely the symmetries of the D3-D5 brane intersection, but lacks that system's localized degrees of freedom, so a decoupling mechanism would be needed for a direct brane realization.

Load-bearing premise

The classification is complete only if the interface carries no independent degrees of freedom, if the allowed interface operators are exactly the local gauge-invariant terms of dimension at most three built from $\partial_\pi g$ and listed in (2.3), and if the supersymmetry transformation is modified only by $\delta_I\psi=(\partial_\pi g)\chi_i\phi_i$; relaxing any of these restrictions could produce additional interface theories.

Editorial extensions

If this is right

Every supersymmetric interface CFT of this type belongs to one of the three families; the classification by rank of $Y_3^\dagger Y_3$ leaves no other possibilities.
In each conformal limit the Poincaré supercharges are doubled, giving supergroups $\mathrm{OSP}(2,2|n)$ with $n=4,2,1$ for the maximal, $N=2$, and $N=1$ theories.
The new theories turn on only supergravity-multiplet operators, so each provides a concrete target for constructing a ten-dimensional supersymmetric Janus-like supergravity solution.
The recovery of the earlier $SU(3)$ interface CFT from the same algebraic system unifies the known interface constructions within a single classification.
The symmetry match with the D3-D5 system, together with the absence of localized degrees of freedom, predicts that any holographic relation between the maximal interface theory and that brane intersection must pass through a decoupling mechanism for the 3-5 strings.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the interface operator list is widened beyond (2.3), for instance by adding higher-dimension operators or localized defect fields, the classification could acquire new branches; the D3-D5 hypermultiplet is a natural candidate for such a branch.
The algebraic structure is tied to $SU(4)\cong SO(6)$, so a similar seven-equation reduction may apply to other codimension-one defects in $N=4$ SYM or to defect theories in related dimensions, where the same $\rho$-matrix identities would do the work.
A practical next step would be to compute two-point functions or anomaly data from the explicit Lagrangians and compare them with the conjectured supergravity duals; the $SO(2)\times SU(2)$ theory has no known brane realization and would be the most surprising target.
The conformal-limit condition (6.3) can be read as a criterion for when a defect coupling is truly marginal: the $(\partial_\pi g)^2$ term must be removable by a field rescaling, a condition that may generalize beyond this specific interface.

Original abstract

We consider theories consisting of a planar interface with $\N=4$ super-Yang-Mills on either side and varying gauge coupling across the interface. The interface does not carry any independent degrees of freedom, but is allowed to support local gauge invariant operators, included with independent interface couplings. In general, both conformal symmetry and supersymmetry will be broken, but for special arrangements of the interface couplings, these symmetries may be restored. We provide a systematic classification of all allowed interface supersymmetries. We find new theories preserving eight and four Poincar\'e supersymmetries, which get extended to sixteen and eight supersymmetries in the conformal limit, respectively with $SU(2) \times SU(2)$, $SO(2) \times SU(2)$ internal symmetry. The Lagrangians for these theories are explicitly constructe d. We also recover the theory with two Poincar\'e supersymmetries and SU(3) internal symmetry proposed earlier as a candidate CFT dual to super Janus. Since our new interface theories have only operators from the supergravity multiplet turned on, dual supergravity solutions are expected to exist. We speculate on the possible relation between the interface theory with maximal supersymmetry and the near-horizon limit of the D3-D5 system.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 6,971 input tokens, $0.0003 reported.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.60 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.77 · compares with prior results 0.79 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

We consider theories consisting of a planar interface with $\N=4$ super-Yang-Mills on either side and varying gauge coupling across the interface. The interface does not carry any independent degrees of freedom, but is allowed to support local gauge invariant operators, included with independent interface couplings. In general, both conformal symmetry and supersymmetry will be broken, but for special arrangements of the interface couplings, these symmetries may be restored. We provide a systematic classification of all allowed interface supersymmetries. We find new theories preserving eight and four Poincar\'e supersymmetries, which get extended to sixteen and eight supersymmetries in the conformal limit, respectively with $SU(2) \times SU(2)$, $SO(2) \times SU(2)$ internal symmetry. The Lagrangians for these theories are explicitly constructe d. We also recover the theory with two Poincar\'e supersymmetries and SU(3) internal symmetry proposed earlier as a candidate CFT dual to super Janus. Since our new interface theories have only operators from the supergravity multiplet turned on, dual supergravity solutions are expected to exist. We speculate on the possible relation between the interface theory with maximal supersymmetry and the near-horizon limit of the D3-D5 system.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We consider theories consisting of a planar interface with $\N=4$ super-Yang-Mills on either side and varying gauge coupling across the interface.	background 0.62	0.48	0.04	asserted 0.97
s1	The interface does not carry any independent degrees of freedom, but is allowed to support local gauge invariant operators, included with independent interface couplings.	background 0.79	0.26	0.04	asserted 0.94
s2	In general, both conformal symmetry and supersymmetry will be broken, but for special arrangements of the interface couplings, these symmetries may be restored.	background 0.92	0.18	0.07	hedged possibility 0.82
s3	We provide a systematic classification of all allowed interface supersymmetries.	contribution 0.98	0.94	0.14	asserted 1.00
s4	We find new theories preserving eight and four Poincar\'e supersymmetries, which get extended to sixteen and eight supersymmetries in the conformal limit, respectively with $SU(2) \times SU(2)$, $SO(2) \times SU(2)$ internal symmetry.	result 0.99	0.96	0.44	asserted 1.00
s5	The Lagrangians for these theories are explicitly constructe d.	contribution 0.64	0.94	0.07	asserted 1.00
s6	We also recover the theory with two Poincar\'e supersymmetries and SU(3) internal symmetry proposed earlier as a candidate CFT dual to super Janus.	result 0.95	0.67	0.11	asserted 0.99
s7	Since our new interface theories have only operators from the supergravity multiplet turned on, dual supergravity solutions are expected to exist.	interpretation 0.98	0.17	0.08	hedged possibility 0.96
s8	We speculate on the possible relation between the interface theory with maximal supersymmetry and the near-horizon limit of the D3-D5 system.	future work 0.62	0.27	0.06	speculative 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.99.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 1.** The discontinuous gauge coupling is replaced by a smoothly v

Figures reproduced from arXiv:hep-th/0603013 by the authors.

References

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hep-th 2025-06 conditional novelty 6.0 of 10

In the 3D Janus background, defect operator dimensions shift by O(c_J^2), and BOPE coefficients are read off as residues of Heun connection coefficients.
Janus and RG-interfaces in minimal 3d gauged supergravity
hep-th 2024-12 conditional novelty 6.0 of 10

New numerical interface solutions in a minimal 3d supergravity model satisfy the proposed universal inequality between transmission and entanglement.
Surface defects in the D4 $-$ D8 brane system
hep-th 2018-07 conditional novelty 6.0 of 10

New exact BPS flows with a running two-form in six-dimensional F(4) supergravity uplift to a warped AdS3 x S2 x S3 massive IIA background interpreted as a surface defect in the AdS6/CFT5 correspondence.
Holographic duals of 3d S-fold CFTs
hep-th 2018-04 accept novelty 6.0 of 10

A class of non-geometric AdS4 string backgrounds is shown to match the three-sphere partition function of a proposed dual 3d N=4 quiver theory, exactly at finite N and in the large-N gravity limit.
Type II origin of dyonic gaugings
hep-th 2016-12 accept novelty 6.0 of 10

The (SO(6)xSO(1,1)) nilpotent dyonic gauging of four-dimensional maximal supergravity lifts to an explicit supersymmetric AdS4 x M5 x S1 S-fold of Type IIB, and the general dyonic CSO(p,q,r) gaugings lift to Type IIA ...
Supersymmetric Janus Solutions in Four Dimensions
hep-th 2013-11 conditional novelty 6.0 of 10

Three families of supersymmetric Janus solutions in four-dimensional N=8 gauged supergravity are constructed, including an argued interface between two distinct G2-symmetric N=1 fixed points carrying opposite internal...
Dual of Big-bang and Big-crunch
hep-th 2006-03 conditional novelty 6.0 of 10

The Janus supergravity solution and its field theory dual are analytically continued to give a gauge theory dual of a big-bang/big-crunch cosmology, whose spacetime singularities are argued to be artifacts of supergravity.
Type IIB Supergravity Action and Holography
hep-th 2026-03 accept novelty 5.5 of 10

A milder topological correction to the PST Type IIB action yields non-vanishing on-shell values matching holography for Lunin-Maldacena and AdS4 S-fold backgrounds.
Holographic reconstruction for defect CFTs from $\mathrm{AdS}_p \times S^q$ spacetimes
hep-th 2026-06 unverdicted novelty 5.0 of 10

Derives holographic one-point functions, stress tensor and Ward identities for defects in AdS5 and AdS6 from AdS2×S2, AdS2×S3 and AdS3×S2 backgrounds in Romans supergravity.
Holographic solutions from 5D $SO(2)\times ISO(3)$ $N=4$ gauged supergravity
hep-th 2025-10 conditional novelty 5.0 of 10

New supersymmetric holographic RG flows, Janus interfaces, black strings and black holes are built in 5D SO(2)×ISO(3) N=4 gauged supergravity and uplifted to M-theory.
($0,6$) AdS$_3$/CFT$_2$ and surface defects
hep-th 2025-04 conditional novelty 5.0 of 10

A brane box and quiver are proposed as the 2d dual of N=(0,6) AdS3 vacua, with a central charge formula and Seiberg-like dualities, though key claims remain conjectural.
Holographic Interfaces in N=4 SYM: Janus and J-folds
hep-th 2020-03 conditional novelty 5.0 of 10

The paper builds five- and ten-dimensional supergravity solutions dual to N=4, N=2, and N=1 Janus interfaces in N=4 super Yang-Mills, plus matching AdS4 J-fold backgrounds, with the N=2 cases being the new content.
On Holographic Defect Entropy
hep-th 2014-03 accept novelty 5.0 of 10

Holographic entanglement entropy for planar defects and boundaries yields a universal defect entropy that decreases monotonically under defect-localized renormalization group flows in the D3/D5 example.
Expectation values of chiral primary operators in holographic interface CFT
hep-th 2012-05 conditional novelty 5.0 of 10

One-point functions of chiral primary operators in an interface version of N=4 super Yang-Mills agree between a classical gauge theory computation and a holographic computation in the limit of large interface charge.

How later papers used it

82 later papers cite it

Evidence: substantial. 66 of the citing papers share no author with it, and 10 of those carry a confident label from Pith's citation classifier.

Pith read 30 of the 140 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

2 later papers by other authors are listed below: 1 built on it and 1 cited it as support. 1 more paper by the same authors is listed: 1 built on it.

Builds on it 2 of 4 papers with this label · 1 by the same authors

Generalized section 6 of this paper to ask whether the Janus configuration can classically be taken to a conformally invariant limit.

Janus Configurations, Chern-Simons Couplings, And The Theta-Angle in N=4 Super Yang-Mills Theory (2008) · 0.94 · paraphrased: the licence does not allow quoting

By the same authors

Proposed a dual gauge theory as a generalization of the interface conformal field theory discussed in this paper.

Exact half-BPS Type IIB interface solutions II: Flux solutions and multi-Janus (2007) (same authors) · 0.94 · paraphrased: the licence does not allow quoting

Cites it as support 1 paper

Deduced from the nontrivial bosonic and fermionic bilinear operators in the dual field theory given in this paper that the scalars should have non-trivial profiles and vanish in the AdS5 asymptotic regions.

Holographic Interfaces in N=4 SYM: Janus and J-folds (2020) · 0.99 · paraphrased: the licence does not allow quoting

How the literature uses it

82 arXiv papers cite this in 138 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 82 sentences without a confident label

Builds on it 4 papers

Now (generalizing section 6 of [ref] ) we would like to ask whether, classically, it is possible to take a limit in which the Janus configuration becomes conformally invariant.

Janus Configurations, Chern-Simons Couplings, And The Theta-Angle in N=4 Super Yang-Mills Theory · Conformally Invariant Limit · 0.94
Later, the Janus field theories in [ref] were generalized to allow the theta-angle to vary which is holographicallly dual to the axion field, and were also applied to construct three-dimensional Chern-Simons theories with $𝒩$ = 4 supersymmetries in [ref] .

Supersymmetric Janus solutions in five and ten dimensions · Introduction · 0.82
In section 8, a dual gauge theory is proposed as a generalization of the interface conformal field theory discussed in [ref] .

Exact half-BPS Type IIB interface solutions II: Flux solutions and multi-Janus · Introduction · 0.94

Uses its method or tool 2 papers

The key step is to generalize $T(SU(n))$ and its close cousins, which we do using Janus domain walls [ref] .

S-Duality of Boundary Conditions In N=4 Super Yang-Mills Theory · Introduction · 0.84
For example, application of the methods developed in [ref] could be used to calculate correlation functions in the presence of the interface/defect. * As the ABJM theory enjoys a well-understood field theoretic CFT description, one may classify the possible interface/defect terms along the lines of [ref] and [ref] , establish their symmetries, and derive the associated supergravity solutions. * In Type IIB theory, the simplest Janus solution breaks all supersymmetries, has a non-trivial dilaton profile, and vanishing 3-form flux fields.

Janus solutions in M-theory · Discussion · 0.81

Compares with it 5 papers

We easily recover the results in Ref. [ref] .

Janus and Multifaced Supersymmetric Theories · Additional Susy Breaking Janus · 0.90
To compare with [ref] , we will look for solutions to eq:susyconditions satisfying the following input assumptions: first, the solutions exist in Minkowski spacetime with the trivial metric, and they preserve a three-dimensional Poincare symmetry.

Supergravity Backgrounds for Four-Dimensional Maximally Supersymmetric Yang-Mills · Janus examples · 0.96
The symmetries of these solutions nicely match with the largest symmetric SYM interfaces classified in [ref] .

Type IIB S-folds: flat deformations, holography and stability · Flat deformations of type IIB S-folds: four-dimensional picture · 0.81

Cites it as support 1 paper

Furthermore, from the presence of nontrivial bosonic and fermionic bilinear operators in the dual field theory [ref] , we deduce that the corresponding scalars, $α$ and $χ$, should both have non-trivial profiles and vanish in the AdS$_5$ asymptotic regions.

Holographic Interfaces in N=4 SYM: Janus and J-folds · The five-dimensional Janus · 0.99

Cites it as background 44 papers

Later, Janus gauge theories were constructed more systematically in [ref] .

Supersymmetric Janus solutions in five and ten dimensions · Introduction · 0.93
It was introduced in [ref] and generalized in [ref] .[See also [ref] for other studies of the supersymmetric Janus theory.] The holographic dual background corresponds to a solution with $Σ$ an infinite strip, which is shown in Figure [ref].

Holographic duals of 3d S-fold CFTs · Supergravity solutions · 0.88
Via the AdS/CFT correspondence [ref] , Janus solutions of supergravity theories [ref] provide a simple and explicit realisation of interfaces in dual field theories [ref] .

S-folds and $AdS_{3}$ flows from the D3-brane · Introduction · 0.94

Discussion

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