Boson-fermion correspondence and holomorphic anomaly equation in 2d Yang-Mills theory on torus

Recently, Okuyama and Sakai proposed a novel holomorphic anomaly equation for the partition function of 2d Yang-Mills theory on a torus, based on an anholomorphic deformation of the propagator in the bosonic formulation. Using the boson-fermion correspondence, we derive the formula for the deformed partition function in fermionic description and give a proof of the holomorphic anomaly equation.

Axion assisted Schwinger effect

We point out an enhancement of the pair production rate of charged fermions in a strong electric field in the presence of time dependent classical axion-like background field, which we call axion assisted Schwinger effect. While the standard Schwinger production rate is proportional to $$ \exp \left(-\pi \left({m}^2+{p}_T^2\right)/E\right) $$ exp − π m 2 + p T 2 / E , with m and pT denoting the fermion mass and its momentum transverse to the electric field E, the axion assisted Schwinger effect can be enhanced at large momenta to exp(−πm2/E). The origin of this enhancement is a coupling between the fermion spin and its momentum, induced by the axion velocity. As a non-trivial validation of our result, we show its invariance under field redefinitions associated with a chiral rotation and successfully reproduce the chiral anomaly equation in the presence of helical electric and magnetic fields. We comment on implications of this result for axion cosmology, focussing on axion inflation and axion dark matter detection.

Renormalization of the flavor-singlet axial-vector current and its anomaly in dimensional regularization

The renormalization constant ZJ of the flavor-singlet axial-vector current with a non-anticommuting γ5 in dimensional regularization is determined to order $$ {\alpha}_s^3 $$ α s 3 in QCD with massless quarks. The result is obtained by computing the matrix elements of the operators appearing in the axial-anomaly equation $$ {\left[{\partial}_{\mu }{J}_5^{\mu}\right]}_R=\frac{\alpha_s}{4\pi }{n}_f{\mathrm{T}}_F{\left[F\tilde{F}\right]}_R $$ ∂ μ J 5 μ R = α s 4 π n f T F F F ˜ R between the vacuum and a state of two (off-shell) gluons to 4-loop order. Furthermore, through this computation, the equality between the $$ \overline{\mathrm{MS}} $$ MS ¯ renormalization constant $$ {Z}_{F\tilde{F}} $$ Z F F ˜ associated with the operator $$ {\left[F\tilde{F}\right]}_R $$ F F ˜ R and that of αs is verified explicitly to hold true at 4-loop order. This equality automatically ensures a relation between the respective anomalous dimensions, $$ {\gamma}_J=\frac{\alpha_s}{4\pi }{n}_f{\mathrm{T}}_F{\gamma}_{FJ} $$ γ J = α s 4 π n f T F γ FJ , at order $$ {\alpha}_s^4 $$ α s 4 given the validity of the axial-anomaly equation which was used to determine the non-$$ \overline{\mathrm{MS}} $$ MS ¯ piece of ZJ for the particular γ5 prescription in use.

Chiral gravitational effect in time-dependent backgrounds

Gravitational counterpart of the chiral magnetic effect, which is referred as the chiral gravitational effect, can also be of interest in a cosmological setup. In this study, we investigate this effect in the time-dependent chiral asymmetric fermion background and in the expanding spacetime by formulating the effective action of gravitational waves. We also analyze the anomaly equation to see how the backreaction from gravitational waves to thermal chiral plasma occurs. We find that the non-trivial time dependence of chiral chemical potential, which can be induced in some scenarios of baryogenesis, is the key ingredient of the chiral gravitational effect. It turns out that the “memory” of the effect is imprinted on the high frequency gravitational waves propagating in the plasma. Cosmological implications and potential effects on the gravitational wave observation are briefly discussed.

Neutrino Anomalies and Chiral Flipping in Anisotropic Einstein-Cartan Cosmology

Recently Palle has investigated the chiral vorticity and Cartan torsion in neutrino asymmetries. In his case he addressed this problem in Goedel s like anisotropic Einstein-Catan cosmology. In this paper we discusse how these ideas applied to sheared Bianchi types I Einstein-Cartan (EC) neutrino amisotropic cosmology, affect the handness of neutrinos in the universe. Actually here a novel concept of the chiral metric is introduced where metric functions also possess two distinct signs as in neutrino flipping or helicity. The axial anomaly equation for neutrinos in the presence of torsion and metric chirality is shown to produce left-handed neutrinos from right-handed torsion. Metric chirality is shown to be able to define how the metric would behave far away of neutrino density. Chiral flipping of the chiral neutrinos in the presence of torsion is also investigated. It is shown that when the chiral torsion is left-handed the chemical chiral potential vanishes as the universe expands.

Curves on K3 surfaces in divisibility 2

We prove a conjecture of Maulik, Pandharipande and Thomas expressing the Gromov–Witten invariants of K3 surfaces for divisibility 2 curve classes in all genera in terms of weakly holomorphic quasi-modular forms of level 2. Then we establish the holomorphic anomaly equation in divisibility 2 in all genera. Our approach involves a refined boundary induction, relying on the top tautological group of the moduli space of smooth curves, together with a degeneration formula for the reduced virtual fundamental class with imprimitive curve classes. We use double ramification relations with target variety as a new tool to prove the initial condition. The relationship between the holomorphic anomaly equation for higher divisibility and the conjectural multiple cover formula of Oberdieck and Pandharipande is discussed in detail and illustrated with several examples.

Holomorphic anomaly equation for and the Nekrasov-Shatashvili limit of local

We prove a higher genus version of the genus $0$ local-relative correspondence of van Garrel-Graber-Ruddat: for $(X,D)$ a pair with X a smooth projective variety and D a nef smooth divisor, maximal contact Gromov-Witten theory of $(X,D)$ with $\lambda _g$ -insertion is related to Gromov-Witten theory of the total space of ${\mathcal O}_X(-D)$ and local Gromov-Witten theory of D. Specializing to $(X,D)=(S,E)$ for S a del Pezzo surface or a rational elliptic surface and E a smooth anticanonical divisor, we show that maximal contact Gromov-Witten theory of $(S,E)$ is determined by the Gromov-Witten theory of the Calabi-Yau 3-fold ${\mathcal O}_S(-E)$ and the stationary Gromov-Witten theory of the elliptic curve E. Specializing further to $S={\mathbb P}^2$ , we prove that higher genus generating series of maximal contact Gromov-Witten invariants of $({\mathbb P}^2,E)$ are quasimodular and satisfy a holomorphic anomaly equation. The proof combines the quasimodularity results and the holomorphic anomaly equations previously known for local ${\mathbb P}^2$ and the elliptic curve. Furthermore, using the connection between maximal contact Gromov-Witten invariants of $({\mathbb P}^2,E)$ and Betti numbers of moduli spaces of semistable one-dimensional sheaves on ${\mathbb P}^2$ , we obtain a proof of the quasimodularity and holomorphic anomaly equation predicted in the physics literature for the refined topological string free energy of local ${\mathbb P}^2$ in the Nekrasov-Shatashvili limit.

Refinement and modularity of immortal dyons

Extending recent results in $$ \mathcal{N} $$ N = 2 string compactifications, we propose that the holomorphic anomaly equation satisfied by the modular completions of the generating functions of refined BPS indices has a universal structure independent of the number $$ \mathcal{N} $$ N of supersymmetries. We show that this equation allows to recover all known results about modularity (under SL(2, ℤ) duality group) of BPS states in $$ \mathcal{N} $$ N = 4 string theory. In particular, we reproduce the holomorphic anomaly characterizing the mock modular behavior of quarter-BPS dyons and generalize it to the case of non-trivial torsion invariant.