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A<sc>bstract</sc> We study 1 + 1-dimensional SU(N) gauge theory coupled to one adjoint multiplet of Majorana fermions on a small spatial circle of circumferenceL. Using periodic boundary conditions, we derive the effective action for the quantum mechanics of the holonomy and the fermion zero modes in perturbation theory up to order (gL)3. When the adjoint fermion mass-squared is tuned tog2N/(2π), the effective action is found to be an example of supersymmetric quantum mechanics with a nontrivial superpotential. We separate the states into theℤNcenter symmetry sectors (universes) labeled byp= 0, . . . ,N– 1 and show that in one of the sectors the supersymmetry is unbroken, while in the others it is broken spontaneously. These results give us new insights into the (1, 1) supersymmetry of adjoint QCD2, which has previously been established using light-cone quantization. When the adjoint mass is set to zero, our effective Hamiltonian does not depend on the fermions at all, so that there are 2N−1degenerate sectors of the Hilbert space. This construction appears to provide an explicit realization of the extended symmetry of the massless model, where there are 22N−2operators that commute with the Hamiltonian. We also generalize our results to other gauge groupsG, for which supersymmetry is found at the adjoint mass-squaredg2h∨/(2π), whereh∨is the dual Coxeter number ofG.
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Lattice Hamiltonian for adjoint QCD2
A<sc>bstract</sc> We introduce a Hamiltonian lattice model for the (1 + 1)-dimensional SU(Nc) gauge theory coupled to one adjoint Majorana fermion of massm. The discretization of the continuum theory uses staggered Majorana fermions. We analyze the symmetries of the lattice model and find lattice analogs of the anomalies of the corresponding continuum theory. An important role is played by the lattice translation by one lattice site, which in the continuum limit involves a discrete axial transformation. On a lattice with periodic boundary conditions, the Hilbert space breaks up into sectors labeled by theNc-alityp= 0, …Nc− 1. Our symmetry analysis implies various exact degeneracies in the spectrum of the lattice model. In particular, it shows that, form= 0 and evenNc, the sectorspandp′ are degenerate if |p−p′| =Nc/2. In theNc= 2 case, we explicitly construct the action of the Hamiltonian on a basis of gauge-invariant states, and we perform both a strong coupling expansion and exact diagonalization for lattices of up to 12 lattice sites. Upon extrapolation of these results, we find good agreement with the spectrum computed previously using discretized light-cone quantization. One of our new results is the first numerical calculation of the fermion bilinear condensate.
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- PAR ID:
- 10570950
- Publisher / Repository:
- Springer
- Date Published:
- Journal Name:
- Journal of High Energy Physics
- Volume:
- 2024
- Issue:
- 8
- ISSN:
- 1029-8479
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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A bstract The mass spectrum of 1 + 1-dimensional SU( N ) gauge theory coupled to a Majorana fermion in the adjoint representation has been studied in the large N limit using Light-Cone Quantization. Here we extend this approach to theories with small values of N , exhibiting explicit results for N = 2 , 3, and 4. In the context of Discretized Light-Cone Quantization, we develop a procedure based on the Cayley-Hamilton theorem for determining which states of the large N theory become null at finite N . For the low-lying bound states, we find that the squared masses divided by g 2 N , where g is the gauge coupling, have very weak dependence on N . The coefficients of the 1 /N 2 corrections to their large N values are surprisingly small. When the adjoint fermion is massless, we observe exact degeneracies that we explain in terms of a Kac-Moody algebra construction and charge conjugation symmetry. When the squared mass of the adjoint fermion is tuned to g 2 N/π , we find evidence that the spectrum exhibits boson-fermion degeneracies, in agreement with the supersymmetry of the model at any value of N .more » « less
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/JHEP08(2024)009
