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Note on massless bosonic states in two-dimensional field theories

Hidenori Fukaya·Masashi Hayakawa·Issaku Kanamori·Hiroshi Suzuki·Tomohisa Takimi
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Abstract

In a wide class of $G_L\times G_R$ invariant two-dimensional super-renormalizable field theories, the parity-odd part of the two-point function of global currents is completely determined by a fermion one-loop diagram. For any non-trivial fermion content, the two-point function possesses a massless pole which corresponds to massless bosonic physical states. As an application, we show that two-dimensional $\mathcal{N}=(2,2)$ supersymmetric gauge theory without a superpotential possesses $U(1)_L\times U(1)_R$ symmetry and contains one massless bosonic state per fixed spatial momentum. The $\mathcal{N}=(4,4)$ supersymmetric pure Yang-Mills theory possesses $SU(2)_L\times SU(2)_R$ symmetry, and there exist at least three massless bosonic states.

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Hidenori Fukaya, Masashi Hayakawa, Issaku Kanamori, Hiroshi Suzuki, Tomohisa Takimi. 2006-12-18. Note on massless bosonic states in two-dimensional field theories. https://doi.org/10.1143/ptp.116.1117

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