2026/08/03 by Sarthak Duary, Sourav Maji · 1 citation
Physics and Astronomy · Mathematics · #hep-th #math-ph #math.MP
39+18 pages
arxiv created 2026/08/03 · arxiv updated 2026/08/05
We study the BRST quantization of the null string after completing its local gauge symmetry by Carroll-Weyl transformations. The resulting worldsheet theory possesses three first-class constraints, C1 = P2, C2 = P ⋅ X', and C3 = P ⋅ X, whose modes realize a Weyl-BMS algebra. The additional Carroll-Weyl constraint qualitatively changes the quantum gauge complex: its scalar s-ghost is intrinsically coupled to the BMS bc-ghost sector, and the anomaly analysis involves three independent cocycles rather than a single Virasoro-type central charge. Starting from the gauge-fixed action, we derive the complete Faddeev-Popov complex, construct the matter and ghost currents and the BRST charge, and evaluate their equal-time operator products in the flipped, equivalently highest-weight, representation. The matter and ghost anomaly coefficients are (cLL,cLS,cSS)matter=(2D,-D,-D) and (cLL,cLS,cSS)ghost=(-54,6,4). Because the corresponding central terms multiply linearly independent ghost bilinears in QB2, BRST nilpotency requires the three conditions D=27, D=6, and D=4, respectively. These conditions are mutually incompatible. Consequently, there is no target-space dimension in which the minimal flat Carroll-Weyl matter-plus-ghost complex is anomaly-free in the highest-weight representation. The familiar D=26 condition of the ILST null string is recovered only after truncation to the two-constraint BMS subsector, which defines a different quantum gauge complex.