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Two-dimensional QCD with Nc colors and Nf flavors of massless fermions in the fundamental representation is expected to exhibit conformal behavior in the infrared governed by a u(Nf) Wess–Zumino–Witten model with level Nc. Using numerical analysis within the lattice formalism with exactly massless overlap fermions, we show the emergence of such behavior in the infrared limit. Both the continuum extrapolated low-lying eigenvalues of the massless Dirac operator and the propagator of scalar mesons exhibit a flow from the ultraviolet to the infrared. We find that the amplitude of the conserved current correlator remains invariant under the flow, while the amplitude of the scalar correlator approaches Nf-independent values in the infrared.
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The spectra of two-dimensional su(2) gauge theories coupled to a single massless Majorana fermion in integer representations, J, are numerically investigated using the discrete light-cone Hamiltonian. One of our aims is to explore the possible presence of massless states for J > 2 in spite of the absence of a continuous symmetry. After comparing to existing results for J = 1 (adjoint fermions), we present results for J = 2, 3, 4. As expected, for J = 2 there are no massless states but in contrast to the J = 1 theory, the lightest state is a boson. We find exact massless modes in the bosonic and fermionic sector for all values of total momentum for J = 3 and J = 4 and, in each sector, the number of massless modes grows with the value of the total momentum. In addition to the spectrum, we present results on the particle number and momentum fraction distributions and argue for a separation of bulk states from edge states.more » « less
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A<sc>bstract</sc> Symmetry algebras deriving from towers of soft theorems can be deformed by a short list of higher-dimension Wilsonian corrections to the effective action. We study the simplest of these deformations in gauge theory arising from a massless complex scalar coupled toF2. The soft gauge symmetry ‘s-algebra’, compactly realized as a higher-spin current algebra acting on the celestial sphere, is deformed and enlarged to an associative algebra containing soft scalar generators. This deformed soft algebra is found to be non-abelian even in abelian gauge theory. A two-parameter family of central extensions of thes-subalgebra are generated by shifting and decoupling the scalar generators. It is shown that these central extensions can also be generated by expanding around a certain non-trivial but Lorentz invariant shockwave type background for the scalar field.more » « less
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A bstract The bulk-to-boundary dictionary for 4D celestial holography is given a new entry defining 2D boundary states living on oriented circles on the celestial sphere. The states are constructed using the 2D CFT state-operator correspondence from operator insertions corresponding to either incoming or outgoing particles which cross the celestial sphere inside the circle. The BPZ construction is applied to give an inner product on such states whose associated bulk adjoints are shown to involve a shadow transform. Scattering amplitudes are then given by BPZ inner products between states living on the same circle but with opposite orientations. 2D boundary states are found to encode the same information as their 4D bulk counterparts, but organized in a radically different manner.more » « less
