Papers
Papers
By me
Coming soon.
AI-generated
For fun, I generate research papers following up on listed extensions in the recent works of some of my favorite physicists. These have not been checked by me for correctness, mainly because I don't have the technical ability to do so yet. They still might be useful to someone, though, so I'm posting them here.
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Follows. Seiberg and Seifnashri, Symmetry Transmutation and Anomaly Matching, especially §6.2, §6.3, and §7.
They replace the usual UV-to-IR group homomorphism,
\varphi\colon G_{\mathrm{UV}}\longrightarrow G_{\mathrm{IR}}by a map of background fields:
B_{\mathrm{IR}}=\Phi(A_{\mathrm{UV}}).For discrete invertible 0-form to 1-form symmetries, they classify \Phi by a central extension, equivalently H^2(G,K), and they identify that with a map of classifying spaces of defect networks. They then leave three things unformulated as one object: \Phi as a higher homomorphism; the noninvertible case, where they say \Phi should be a map of tube algebras because there are no ordinary background gauge fields; and continuous symmetries with nonflat backgrounds (the FQHE formula B=\mathrm{d}A), which topological defect networks do not capture.
The draft defines a single background stack with connections on top-dimensional strata and (possibly noninvertible) defects on lower strata. An RG wall supplies a kernel of junction spaces. If that kernel is representable on the transmitted IR sector, Yoneda produces a symmetric-monoidal map \Phi, unique up to contractible choice; right-principality of the IR wall action is a sufficient condition. Restrictions of this one map recover the classifying-space map, including the central-extension obstruction BG\to B^2K; a tube-algebra homomorphism, by annularizing a strong unitary pivotal tensor functor on codimension-one defects; and a morphism of connection stacks that keeps curvature and gauge descent. Anomaly matching is separate: it needs a local Wilsonian factorization with a pointwise-nonzero determinant-line map, after which the UV anomaly is the pulled-back IR anomaly tensored with the wall contribution. The note does not construct the wall for any specific RG flow; a concrete theory still has to supply that representation.
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Follows. Seiberg and Seifnashri, Symmetry Transmutation and Anomaly Matching, Appendix B.
For ordinary 0-form to p-form transmutation they classify the background map by H^{p+1}(BG,K). Appendix B then says there should also be maps that depend on tangent-bundle characteristic classes (Stiefel–Whitney classes of TM) and therefore do not factor through BG alone.
This note does not construct such a transmutation. It classifies simultaneous A_4 0-form and calibrated \mathbb{Z}_2^{(1)} symmetries in one 1+1d bosonic lattice gauge theory on unoriented O(2) surfaces. Both symmetries are present at every scale, so the graph is fractionalization data, not a UV-to-IR transmutation. Inside the class of finite-depth source-covariant conjugates of one gapped Hamiltonian, and for graphs with characteristic descent, the pointed law is classified by the relative mapping 2-type
\operatorname{Map}\!\left( (BA_4\times BO(2),\{*\}\times BO(2)), (B^2\mathbb{Z}_2,*) \right).That type is \{0,\omega\}. Here \omega is the binary-tetrahedral class of
1\longrightarrow\mathbb{Z}_2\longrightarrow SL(2,3) \longrightarrow A_4\longrightarrow 1.The mixed term that would carry the tangent dependence vanishes:
H^1(BA_4;\mathbb{Z}_2)\otimes H^1(BO(2);\mathbb{Z}_2)=0,since H^1(BA_4;\mathbb{Z}_2)=0. The background law is therefore
B=c\,\omega(A),\qquad c\in\mathbb{Z}_2.On \mathbb{RP}^2, one can turn on the two classes at once:
\omega(A)\neq 0,\qquad w_1^2=w_2\neq 0.A finite-coupling partition function still only sees the ordinary component. The dynamical transmutation version of the problem is left open: that would need a model whose symmetry content actually changes with scale.
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Follows. Komargodski, Miscioscia, and Popov, Regge's Inferno, especially §1.2.
KMP show that the large-spin limits of a CFT on the Lorentzian cylinder, taking J_z\to\infty at fixed \tau/\sqrt{J_z} in three dimensions, or J_1,J_2\to\infty at fixed J_1/J_2 and \tau/(J_1J_2)^{1/3} in four, are governed by plane waves with an emergent Heisenberg symmetry. They derive the universal extensive thermodynamics from that symmetry alone and list five calculations it leaves open: correlators, thermal nonanalyticity, causality and positive energy, supersymmetry and indices, and a large-N gravity dual with pp-wave boundary conditions.
This note works through all five. Heisenberg symmetry alone fixes the vacuum two-point function transported to the pp wave as a Mehler kernel,
\widetilde G_p(T)= {2\pi C_\mathcal{O} e^{i\pi\Delta/2}\over\Gamma(\Delta)} {\Theta(p\sin T)|p|^{\Delta-1}\over|\sin T|^\Delta} \exp\!\left[-ip\,{(|z_1|^2+|z_2|^2)\cos T-2z_1\cdot z_2\over\sin T}\right],and fixes the selection rules and orbit dependence of heavy-state correlators, though the reduced OPE matrices they act on remain theory-specific data. Taking the angular velocities of Kerr–AdS to the speed of light gives the boundary pressures
\mathcal F_3(r)={(r^2-1)^2\over16\pi G_4 r},\qquad \mathcal F_4(r)={(r^2-1)^3\over16\pi G_5 r^2},which are non-analytic at T_c=1/(2\pi), with second- and third-order Ehrenfest transitions respectively; their Legendre–Fenchel transforms give the large-spin entropy functions. The pp waves are stably causal but not globally hyperbolic, and the conformal net inherited from the cylinder is microcausal with a self-adjoint time generator; positivity of the double-spin Hamiltonian reduces, case by case, to the all-representation bound \Delta\geq\max(k,\bar k), which is left as a conjecture. For a chosen superconformal algebra and R-charge ray, the surviving superalgebra is identified as the zero-grade centralizer of the contraction. Finally, the note exhibits exact Kerr–AdS_4 and Kerr–AdS_5 metrics whose conformal boundaries are exactly the KMP pp waves, giving the large-N gravity duals KMP ask for.