Domain walls and M2-branes partition functions: M-theory and ABJM Theory

M.Nouman Muteeb

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Domain walls and M2-branes partition functions: M-theory and ABJM Theory

M.Nouman Muteeb

High Energy Physics - Theory · Submitted 8 Oct 2020

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

The authors' main claim The M-string degrees of freedom on the domain walls are interpreted in terms of a pair of interacting supersymmetric WZW models.

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We study the BPS counting functions (free energies) of the M-string configurations. We consider separated M5-branes along with M2-branes stretched between them, with M5-branes acting as domain walls interpolating different configurations of M2-branes. We find recursive structure in the free energies of these configurations. The M-string degrees of freedom on the domain walls are interpreted in terms of a pair of interacting supersymmetric WZW models. We also compute the elliptic genus of the M-string in a toy model of the ABJM theory and compare it with the M-theory computation.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We study the BPS counting functions (free energies) of the M-string configurations.	contribution 0.99	0.92	0.08	asserted 0.84
s1	We consider separated M5-branes along with M2-branes stretched between them, with M5-branes acting as domain walls interpolating different configurations of M2-branes.	method 0.50	0.44	0.06	asserted 0.94
s2	We find recursive structure in the free energies of these configurations.	result 1.00	0.96	0.34	asserted 1.00
s3	The M-string degrees of freedom on the domain walls are interpreted in terms of a pair of interacting supersymmetric WZW models.	interpretation 1.00	0.84	0.22	asserted 0.99
s4	We also compute the elliptic genus of the M-string in a toy model of the ABJM theory and compare it with the M-theory computation.	contribution 0.72	0.95	0.11	asserted 1.00

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We study the BPS counting functions (free energies) of the M-string configurations. We consider separated M5-branes along with M2-branes stretched between them, with M5-branes acting as domain walls interpolating different configurations of M2-branes. We find recursive structure in the free energies of these configurations. The M-string degrees of freedom on the domain walls are interpreted in terms of a pair of interacting supersymmetric WZW models. We also compute the elliptic genus of the M-string in a toy model of the ABJM theory and compare it with the M-theory computation.

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Evaluating the residue of ([ref]) on these poles we get Z_^2^ABJM=∑∏^x1x_2,y_1y_2_(x_1,y_1)∈Y,(x_2,y_2)∈Y^t θ_1((x_1-x_2)ϵ_1+(y_1-y_2)ϵ_2)θ_1((x_1-x_2-1)ϵ_1+(y_1-y_2-1)ϵ_2)/θ_1((x_1-x_2-1)ϵ_1+(y_1-y_2)ϵ_2)θ_1((x_1-x_2)ϵ_1+(y_1-y_2+1)ϵ_2) =∏θ_1(ϵ_1)θ_1(ϵ_2)/θ_1^'θ_1(ϵ_1+ϵ_2) ∑∏_(x_1,y_1)∈Y,(x_2,y_2)∈Y^t ×θ_1((x_1-x_2)ϵ_1+(y_1-y_2)ϵ_2)θ_1((x_1-x_2-1)ϵ_1+(y_1-y_2-1)ϵ_2)/θ_1((x_1-x_2-1)ϵ_1+(y_1-y_2)ϵ_2)θ_1((x_1-x_2)ϵ_1+(y_1-y_2+1)ϵ_2) This can be written in the canonical form by using the theorem (2.11) of reference [ref] ∑_(x_1,y_1)∈Yt_1^x_1t_2^y_1+∑_(x_2,y_2)∈Y^tt_1^1-x_2t_2^1-y_2- (∑_(x_1,y_1)∈Yt_1^x_1-λ^t_y_1(Y^t)t_2^1-y_1+λ_x_1(Y)+ ∑_(x_2,y_2)∈Y^tt_1^1-x_2+λ^t_y_2(Y)t_2^y_2-λ_x_2(Y^t))= ∑_(x_1,y_1)∈Y,(x_2,y_2)∈Y^tt_1^x_1-x_2t_2^y_1-y_2(1-t_1)(1-t_2) as Z_^2^ABJM=∏θ_1(ϵ_1)θ_1(ϵ_2)/θ_1^'θ_1(ϵ_1+ϵ_2) ∑_Y,Y^t∏_(x_1,y_1)∈Y,(x_2,y_2)∈Y^t ×θ_1(x_1ϵ_1-y_1ϵ_2)θ_1((1-x_2)ϵ_1-(1-y_2)ϵ_2)/θ_1((x_1-

Instanton counting on blowup. I. 4-dimensional pure gauge theory · N$≥$ 2 · 0.92
We will use instead a prescription given in [ref] for the case of $N=2$.

2d Index and Surface operators · ABJM model vs M-theory · 0.99

Compares with 2 papers

For ABJM theory and for $N=1$ we get the expression Z^ABJM_^2=θ_1(m+ϵ_+)θ_1(m-ϵ_+)/θ_1(ϵ_1)θ_1(ϵ_2) This expression matches with its $Z^M-string_^2$ [ref] .

M-Strings · ABJM model vs M-theory · 0.98
The expression ([ref]) is reminiscent of the $𝒩=2$ minimal model product representation of the elliptic genus [ref] .

On the Landau-Ginzburg Description of $N=2$ Minimal Models · Domain wall degrees of freedom: coupled supersymmetric WZW models · 0.96

Cites as support 1 paper

This recursive structure, as shown in [ref] , indicates that the degrees of freedom corresponding to the $F^1_1,1_2,...,1_N(τ,m,ϵ_1,ϵ_2)$ can be obtained from $F^1_1,0,...,0(τ,m,ϵ_1,ϵ_2)$ upto the $univeral$ factor $W(τ,m,ϵ_1,ϵ_2)$.

Self-Duality and Self-Similarity of Little String Orbifolds · Remark : Some comments on the algebra of holomorphic curves and the recursive structure · 0.96

Cites as background 5 papers

The supergroup WZW model [ref] is described by the maps $f:Σ→(super group)$ from a two dimensional Euclidean Riemann surface $Σ$ to the supergroup $SG$ and its dynamics is given by the action S[f]=-k/8π∫_Σd^2x(f^-1∂^αf,f^-1∂_αf)- ik/24πd^3xϵ^μνλ(f^-1∂_μf,[f^-1∂_νλ,f^-1∂_λf]) where $$ is a three-manifold with $Σ$ as its boundary and $k∈ℤ$ is the level.

Topological M-Strings and Supergroup WZW Models · Domain wall degrees of freedom: coupled supersymmetric WZW models · 0.96
The supergroup WZW model [ref] is described by the maps $f:Σ→(super group)$ from a two dimensional Euclidean Riemann surface $Σ$ to the supergroup $SG$ and its dynamics is given by the action S[f]=-k/8π∫_Σd^2x(f^-1∂^αf,f^-1∂_αf)- ik/24πd^3xϵ^μνλ(f^-1∂_μf,[f^-1∂_νλ,f^-1∂_λf]) where $$ is a three-manifold with $Σ$ as its boundary and $k∈ℤ$ is the level.

Mock Modular Index of M2-M5 Brane System · Domain wall degrees of freedom: coupled supersymmetric WZW models · 0.96
For details we refer the reader to [ref] .

Self-dual Strings and 2D SYM · ABJM model vs M-theory · 0.97

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