On Domain Walls of N=1 Supersymmetric Yang-Mills in Four Dimensions

Bobby Acharya; Cumrun Vafa

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On Domain Walls of N=1 Supersymmetric Yang-Mills in Four Dimensions

Bobby Acharya, Cumrun Vafa

High Energy Physics - Theory · Submitted 1 Mar 2001

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim This leads to a counting of BPS degeneracies of domain walls in agreement with expected results.

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We study the BPS domain walls of supersymmetric Yang-Mills for arbitrary gauge group. We describe the degeneracies of domain walls interpolating between arbitrary pairs of vacua. A recently proposed large N duality sheds light on various aspects of such domain walls. In particular, for the case of G = SU(N) the domain walls correspond to wrapped D-branes giving rise to a 2+1 dimensional U(k) gauge theory on the domain wall with a Chern-Simons term of level N. This leads to a counting of BPS degeneracies of domain walls in agreement with expected results.

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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 study the BPS domain walls of supersymmetric Yang-Mills for arbitrary gauge group.	contribution 1.00	0.91	0.09	asserted 0.95
s1	We describe the degeneracies of domain walls interpolating between arbitrary pairs of vacua.	contribution 0.90	0.88	0.13	asserted 0.99
s2	A recently proposed large N duality sheds light on various aspects of such domain walls.	background 0.91	0.10	0.07	asserted 0.77
s3	In particular, for the case of G = SU(N) the domain walls correspond to wrapped D-branes giving rise to a 2+1 dimensional U(k) gauge theory on the domain wall with a Chern-Simons term of level N.	result 0.58	0.30	0.40	asserted 1.00
s4	This leads to a counting of BPS degeneracies of domain walls in agreement with expected results.	result 0.85	0.69	0.44	asserted 0.95

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.50.

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The paper

Original abstract

We study the BPS domain walls of supersymmetric Yang-Mills for arbitrary gauge group. We describe the degeneracies of domain walls interpolating between arbitrary pairs of vacua. A recently proposed large N duality sheds light on various aspects of such domain walls. In particular, for the case of G = SU(N) the domain walls correspond to wrapped D-branes giving rise to a 2+1 dimensional U(k) gauge theory on the domain wall with a Chern-Simons term of level N. This leads to a counting of BPS degeneracies of domain walls in agreement with expected results.

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Cited by 21 Pith papers

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How the literature uses it

42 arXiv papers cite this in 80 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 · 51 sentences without a confident label

Builds on it 2 papers

In this section we will derive a full generalization of the Acharya-Vafa formula [ref] while staying in field theory framework.

Degenerate Domain Walls in Supersymmetric Theories · SYM on a cylinder: Moduli and symmetries · 1.00
In particular, starting with a known $𝒩=2$ enhancement point of the $T_𝒩=1[L(p,1)]$ theory [ref] , we propose a quiver description for the $T_𝒩=1[L(p,q)]$ theory.

Higher-Form Symmetries, Bethe Vacua, and the 3d-3d Correspondence · 3d $𝒩=1$ · 0.80

Uses its method or tool 1 paper

Indices for such theories are computed in [ref] , following [ref] .[Deforming to $𝒩=3$ Yang-Mills theory might be physically more natural, considering the origin of M2-brane theories from $𝒩=3$ D-brane systems.

Supersymmetric vacua of mass-deformed M2-brane theory · Introduction and discussions · 0.82

Uses its data or values 2 papers

Indeed, for the AV CS theory the Witten index was computed in [ref] and was found to be proportional to $1/(N-k)!$.

Brane Dynamics and 3D Seiberg Duality on the Domain Walls of 4D N=1 SYM · Pseudo-moduli, the s-rule and brane creation · 0.86
For these 3d $𝒩 = 1$ Chern-Simons theories $T_𝒩 = 1[L(p,q)]$ the Witten index was computed in [ref] to be I_T^3(T_𝒩 = 1[L(p,q),U(N)]) = p N .

An $\mathcal{N}=1$ 3d-3d Correspondence · Specializing $M_3$: $T_𝒩 = 1[L(p,q), U(N)]$ · 0.96

Compares with it 6 papers

After T-duality this setup bears many similarities with the large-$N$ dual string theory background of [ref] but is not identical to it.

Brane Dynamics and 3D Seiberg Duality on the Domain Walls of 4D N=1 SYM · Introduction · 0.91
As we have already mentioned in the Introduction, for $k=1$ the obtained action is level/rank dual [ref] to the Acharya-Vafa [ref] worldvolume theory of the $k=1$ domain wall, but differs from the latter for $k>1$.

Supermembranes and domain walls in $\mathcal N=1$, $D=4$ SYM · Membrane coupled to SYM · 0.98
The effective theory in this vacuum agrees with the theory that Acharya and Vafa (AV) discovered to govern the dynamics on domain walls in $SU(N)$ SYM [ref] .

Living on the walls of super-QCD · Introduction and summary of results · 0.85

Cites it as support 2 papers

Assuming that this is the case, the rest of the anomaly corresponding to $ν'=ν-1=G-1$ is accounted for by the TQFT living on the domain wall.[It requires some computation to determine that the goldstino corresponds to $ν=1$ rather than $ν=-1$. ] In fact, it was argued that some TQFT does live on the domain wall [ref] .

On time-reversal anomaly of 2+1d topological phases · Semion-fermion theory on a SYM domain wall · 0.98
However, from various indirect field theory arguments in [ref] as well as successful applications of Yang-Mills Chern-Simons index on $T^2$ to D-branes living on uncompactified $ℝ^2+1$ [ref] , we believe that our calculation also provides the vacuum counting for M2-branes living on $ℝ^2+1$.

Supersymmetric vacua of mass-deformed M2-brane theory · Introduction and discussions · 1.00

Cites it as background 12 papers

Nevertheless, in the recent years our understanding of these theories has overcome a new twist [ref] (see also [ref] for earlier considerations).

Phases of $\mathcal{N}=1$ Quivers in $2+1$ Dimensions · Introduction · 0.83
This question has been analyzed in great detail by Acharya and Vafa [ref] .

Living on the walls of super-QCD · Domain walls of SYM: a review · 0.95
Holographically, domain walls are described by 5-branes wrapping compact 3-cycles of the internal geometry, with the other three directions being along $ℝ^1,3$ [ref] (see also [ref] for a construction within the KS model).

Confinement in a finite duality cascade · Domain walls - holographic description · 0.83

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