arXiv subjects

Harsh Anand

Publications and source records attributed to Harsh Anand.

3 recordsLinked to original sources

arXiv2026

From $Z$ to $a$: High-temperature relations, subleading semi-universality, and conformal anomalies

The free energy of any CFT, $ \ln Z(\beta; \omega_i)$, admits two expansions: high temperature ($\beta \rightarrow 0$) and fast rotation ($\omega_i \rightarrow 1$). We demonstrate that locality of the thermal effective action forces $\ln Z$ to take a simple analytic form at all orders in the high temperature expansion, and further imposes an infinite number of sharp relations on the coefficients in this expansion. All are homogeneous, except at order $\beta^1$ due to the Weyl anomaly. From this, the $a$-anomaly can be extracted from the partition function. The relations resum in the fast-spinning expansion into differential equations in $\beta$ obeyed by the semi-universal limit and its corrections. We verify the relations in a variety of CFTs. We generalize to any even $d$, but find no similar relations at odd $d$.

hep-th↗

arXiv2026

Coupling Higher Form Structures of the EFT of Force Free Electrodynamics to Gravity

The charged Reissner Nordstr$\"{o}$m black hole metric is obtained from the Einstein Hilbert action. This action has the kinetic term $F^2 = (da)^2$. Motivated by the higher-form symmetry structure of the EFT of Force Free Electrodynamics, we replace the Maxwell field-strength in the EH action by the gauge-invariant combination $(b-da)^2$, where $a_\mu$ is the gauge field and $b_{\mu\nu}$ is a background two-form field which is closed, that is, $db =0$. This ensures that the new action has a higher form symmetry $b \rightarrow b+d\Lambda, a\rightarrow a+\Lambda$. Here, unlike in qed, $\Lambda$ may be any one form (not necessarily a differential one form $\partial_\mu \phi$). The higher form symmetry here is one with the conserved current being a two form and the charge integrated on surfaces. It is the current of vector field lines that is conserved here, not the current of particles. Thus, integrating over a surface through which the field lines pierce is sufficient to find the number of these lines that are passing through; so the charge is integrated on surfaces, rather than on the volume. By fixing a gauge for $a_\mu$ and $b_{\mu\nu}$, we obtain the black-hole metric dual to the boundary theory of FFE. There are two different starting points: 1)Consider the $b$ to be exact. The bulk dual to this theory is the RN geometry. 2)Consider the $b$ to have a Dirac Like Monopole and thus to not be exact ($b \neq dc$ for any $c$). This again does not lead to a new bulk dual, it leads us to the Dyonic RN geometry (which arises in the E-M theory when $a$ has the monopole term). Thus, Einstein-FFE leads to the known RN and dyonic solutions of the E-M theory. We note that AdS-CFT applied to this problem states that since the boundary EFT of FFE describes the same theory of a sector of strongly magnetised QED plasma, bulk E-FFE reproduces the same solutions of E-M theory.

hep-th↗

arXiv2025

Semi-universality of CFT$_d$ entropy at large spin

The thermal partition function, $Z$, of a $CFT_d$ on $S^{d-1}$ is parameterized by the inverse temperature $\beta$ along with $\lfloor d/2\rfloor$ angular velocities $\omega_i$. In this paper, we investigate the behaviour of this partition function when $n$ of the $\omega_i$ are scaled to unity (the largest allowed value) at fixed values of the other $(\lfloor d/2\rfloor-n)$ angular velocities. We argue that $\ln Z$ develops a simple pole in $(1-\omega_i)$ for each $\omega_i$ that is scaled to unity. The residue of this product of poles is a theory dependent (so non-universal) function of $\beta$ and the fixed angular velocities. The inverse Laplace transformation of this partition function constrains the functional form of the field theory entropy as a function of charges in a limit in which angular momenta and the twist are scaled as follows. While $n$ special angular momenta $J_1\ldots J_n$ are scaled to infinity, the twist and the other angular momenta - collectively denoted $x_i$ - are also taken to infinity but at the slower rate that ensures that the scaled charges $x_i/(J_1 J_2 \ldots J_n)^{\frac{1}{n+1}}$ are held fixed. In this limit, we demonstrate that the scaled entropy $S/(J_1 J_2 \ldots J_n)^{\frac{1}{n+1}}$ depends only on the $\lfloor d/2\rfloor-n+1$ scaled charges defined above (the precise form of this dependence is non-universal). We verify our predictions (and compute all non-universal functions) in the case of free scalar theories (which show surprisingly rich behaviour) as well as large $N$, strongly coupled ${\cal N}=4$ Yang Mills theory. The last theory is analyzed in the bulk via the AdS/CFT correspondence. In the scaling limit described above, its phase diagram displays sharp phase transitions between black hole, grey galaxy, and thermal gas phases.

hep-th↗