Gaugino condensates in 𝒩=1 super-Yang-Mills Theory on Eguchi-Hanson space
Abstract
We study gaugino condensates in 𝒩=1 SU(N) super-Yang--Mills theory on Eguchi--Hanson space using instanton methods. Fractional topological charge and the spectral asymmetry of the asymptotic ℝℙ3 boundary modify the instanton calculus. A charge-1/2 instanton carries only two adjoint gaugino zero modes and can therefore contribute directly to the bilinear. Because the Eguchi--Hanson path integral prepares a boundary state on ℝℙ3, the observables are boundary-sector-projected amplitudes. Moreover, supersymmetric Ward identities ensure that chiral correlators are independent of insertion points and the Eguchi--Hanson resolution parameter. For SU(2) instanton, with central holonomy, the full collective-coordinate integral gives ⟨tr(λλ)⟩=16π2Λ3 for a specified boundary projection, reproducing the flat-space value. For a single SU(2)-block embedding in SU(N>2), the noncentral holonomy requires a continuum determinant for renormalization-group invariance, so zero modes alone do not determine the bilinear. We also study a charge-$1$ SU(4) two-block saddle with central holonomy, $16$ bosonic moduli, and $8$ adjoint zero modes. Its collective-coordinate integral gives ⟨∏i=14tr(λλ)(xi)⟩=1/6(16π2Λ3)4. Under the assumptions required for position independence and clustering, this result determines the fourth power of the bilinear condensate in the corresponding boundary sector. Since no independent bilinear calculation is available in the same sector, the factor 1/6 does not by itself constitute a clustering puzzle.
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BibTeX
@misc{anber2026gaugino,
title = {{Gaugino condensates in $\mathcalN=1$ super-Yang-Mills Theory on Eguchi-Hanson space}},
author = {Mohamed M. Anber},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.00486},
eprint = {2610.00486},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.00486},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Gaugino condensates in 𝒩=1 super-Yang-Mills Theory on Eguchi-Hanson space
AU - Mohamed M. Anber
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.00486
UR - https://arxiv.org/abs/2610.00486
AB - We study gaugino condensates in 𝒩=1 SU(N) super-Yang--Mills theory on Eguchi--Hanson space using instanton methods. Fractional topological charge and the spectral asymmetry of the asymptotic ℝℙ^3 boundary modify the instanton calculus. A charge-1/2 instanton carries only two adjoint gaugino zero modes and can therefore contribute directly to the bilinear. Because the Eguchi--Hanson path integral prepares a boundary state on ℝℙ^3, the observables are boundary-sector-projected amplitudes. Moreover, supersymmetric Ward identities ensure that chiral correlators are independent of insertion points and the Eguchi--Hanson resolution parameter. For SU(2) instanton, with central holonomy, the full collective-coordinate integral gives ⟨tr(λλ)⟩=16π^2Λ^3 for a specified boundary projection, reproducing the flat-space value. For a single SU(2)-block embedding in SU(N>2), the noncentral holonomy requires a continuum determinant for renormalization-group invariance, so zero modes alone do not determine the bilinear. We also study a charge-$1$ SU(4) two-block saddle with central holonomy, $16$ bosonic moduli, and $8$ adjoint zero modes. Its collective-coordinate integral gives ⟨∏_i=1^4tr(λλ)(x_i)⟩=1/6(16π^2Λ^3)^4. Under the assumptions required for position independence and clustering, this result determines the fourth power of the bilinear condensate in the corresponding boundary sector. Since no independent bilinear calculation is available in the same sector, the factor 1/6 does not by itself constitute a clustering puzzle.
ER -