An anomalous transformation in string field theory |
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| Institution: | 1. International Center for Quantum Materials and School of Physics, Peking University, Beijing 100871, China;2. Collaborative Innovation Center of Quantum Matter, Beijing 100871, China;3. CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China;4. Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China;1. Institute for Advanced Study, Tsinghua University, Beijing 100084, China;2. Department of Physics, University of California, San Diego, CA 92093, USA;1. Philippe Meyer Institute, Physics Department, École Normale Supérieure, PSL Research University, 24 rue Lhomond, F-75231 Paris Cedex 05, France;2. University of Graz, Institute for Physics, A-8010 Graz, Austria |
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| Abstract: | Conformal field theory techniques are used to analyze a recently proposed transformation of Witten's interaction vertex from center-of-mass to mid-point variables. As presented in the literature the transformed vertex has the surprising property of being non-local in the mid-point coordinates unless an additional non-unitary transformation is performed. This renders the kinetic term non-local and poses additional problems. Here we show that, besides being non-local, the transformed vertex does not satisfy the overlap equations and fails to be BRST invariant. These bad properties are the result of an associativity anomaly of the type considered by Horowitz and Strominger. However, this anomaly is “almost trivial” in the sense that most of its bad effects can be avoided by choosing a proper regularization. |
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