Abstract
In recent work, we demonstrated that the confined-phase spectrum of non-supersymmetric pure Yang-Mills theory coincides with the spectrum of the chiral sector of a two-dimensional conformal field theory in the large-$N$ limit. This was done within the tractable setting in which the gauge theory is compactified on a three-sphere whose radius is small compared to the strong length scale. In this paper, we generalize these observations by demonstrating that similar results continue to hold even when massless adjoint matter fields are introduced. These results hold for both thermal and $(-1)^F$-twisted partition functions, and collectively suggest that the spectra of large-$N$ confining gauge theories are organized by the symmetries of two-dimensional conformal field theories.
Highlights
In the large-N limit, QCD and other 4D confining gauge theories become free in terms of their physical degrees of freedom [1, 2]
In recent work, we demonstrated that the confined-phase spectrum of nonsupersymmetric pure Yang-Mills theory coincides with the spectrum of the chiral sector of a two-dimensional conformal field theory in the large-N limit
In recent work [4], we focused on the case of pure non-supersymmetric Yang-Mills (YM) theory, and within an especially tractable setting we demonstrated that its confined-phase spectrum coincides with the spectrum of the chiral sector of a two-dimensional conformal field theory (CFT) in the large-N limit
Summary
In the large-N limit, QCD and other 4D confining gauge theories become free in terms of their physical degrees of freedom [1, 2]. Our observations suggest that the large-N confined-phase spectra of 4D gauge theories are controlled by infinite-dimensional spectrum-generating algebras which include at least the Virasoro algebra, at least in the small RΛ limit. [9, 10] are possible because the large-N confined-phase partition functions of gauge theories on S3 × S1 can be expressed as combinations of modular and Jacobi forms This surprising “modularity” is an important ingredient governing the spectra of such theories, and enables these 4D partition functions to coincide with the chiral torus partition functions of 2D CFTs, as claimed in eq (1.1). Several appendices are included which define the notation and conventions that we shall be using throughout this paper and which provide further details concerning some of the results derived
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