More Like this

1. Ordinary modules for vertex algebras of 𝔬𝔰𝔭 _1|2𝑛

   https://doi.org/10.1515/crelle-2024-0060  

   Creutzig, Thomas; Genra, Naoki; Linshaw, Andrew (August 2024, Journal für die reine und angewandte Mathematik (Crelles Journal))

   Abstract We show that the affine vertex superalgebra $V^k\left(\mathfrak{o}\mathfrak{s}{\mathfrak{p}}_{1|2n}\right)$V^{k}(\mathfrak{osp}_{1|2n})at generic level 𝑘 embeds in the equivariant 𝒲-algebra of $\mathfrak{s}{\mathfrak{p}}_{2n}$\mathfrak{sp}_{2n}times $4n$4nfree fermions.This has two corollaries:(1) it provides a new proof that, for generic 𝑘, the coset $\mathrm{Com}(V^k\left(\mathfrak{s}{\mathfrak{p}}_{2n}\right),V^k\left(\mathfrak{o}\mathfrak{s}{\mathfrak{p}}_{1|2n}\right))$\operatorname{Com}(V^{k}(\mathfrak{sp}_{2n}),V^{k}(\mathfrak{osp}_{1|2n}))is isomorphic to ${\mathcal{W}}^{\mathrm{\ell }}\left(\mathfrak{s}{\mathfrak{p}}_{2n}\right)$\mathcal{W}^{\ell}(\mathfrak{sp}_{2n})for $\mathrm{\ell }=-\left(n+1\right)+\left(k+n+1\right)/\left(2k+2n+1\right)$\ell=-(n+1)+(k+n+1)/(2k+2n+1), and(2) we obtain the decomposition of ordinary $V^k\left(\mathfrak{o}\mathfrak{s}{\mathfrak{p}}_{1|2n}\right)$V^{k}(\mathfrak{osp}_{1|2n})-modules into $V^k\left(\mathfrak{s}{\mathfrak{p}}_{2n}\right)\otimes {\mathcal{W}}^{\mathrm{\ell }}\left(\mathfrak{s}{\mathfrak{p}}_{2n}\right)$V^{k}(\mathfrak{sp}_{2n})\otimes\mathcal{W}^{\ell}(\mathfrak{sp}_{2n})-modules.Next, if 𝑘 is an admissible level and ℓ is a non-degenerate admissible level for $\mathfrak{s}{\mathfrak{p}}_{2n}$\mathfrak{sp}_{2n}, we show that the simple algebra $L_k\left(\mathfrak{o}\mathfrak{s}{\mathfrak{p}}_{1|2n}\right)$L_{k}(\mathfrak{osp}_{1|2n})is an extension of the simple subalgebra $L_k\left(\mathfrak{s}{\mathfrak{p}}_{2n}\right)\otimes {\mathcal{W}}_{\mathrm{\ell }}\left(\mathfrak{s}{\mathfrak{p}}_{2n}\right)$L_{k}(\mathfrak{sp}_{2n})\otimes{\mathcal{W}}_{\ell}(\mathfrak{sp}_{2n}).Using the theory of vertex superalgebra extensions, we prove that the category of ordinary $L_k\left(\mathfrak{o}\mathfrak{s}{\mathfrak{p}}_{1|2n}\right)$L_{k}(\mathfrak{osp}_{1|2n})-modules is a semisimple, rigid vertex tensor supercategory with only finitely many inequivalent simple objects.It is equivalent to a certain subcategory of ${\mathcal{W}}_{\mathrm{\ell }}\left(\mathfrak{s}{\mathfrak{p}}_{2n}\right)$\mathcal{W}_{\ell}(\mathfrak{sp}_{2n})-modules.A similar result also holds for the category of Ramond twisted modules.Due to a recent theorem of Robert McRae, we get as a corollary that categories of ordinary $L_k\left(\mathfrak{s}{\mathfrak{p}}_{2n}\right)$L_{k}(\mathfrak{sp}_{2n})-modules are rigid. 

   more » « less
2. Computation of the expectation value of the spin operator ${\hat{S}}^2$ for the spin-flip Bethe–Salpeter equation

   https://doi.org/10.1088/2516-1075/ad48ed  

   Barker, B A; Seshappan, A; Strubbe, D A (May 2024, Electronic Structure)

   Abstract Spin-flip (SF) methods applied to excited-state approaches like the Bethe–Salpeter equation allow access to the excitation energies of open-shell systems, such as molecules and defects in solids. The eigenstates of these solutions, however, are generally not eigenstates of the spin operator ${\hat{S}}^2$. Even for simple cases where the excitation vector is expected to be, for example, a triplet state, the value of $⟨{\hat{S}}^2⟩$may be found to differ from 2.00; this difference is called ‘spin contamination’. The expectation values $⟨{\hat{S}}^2⟩$must be computed for each excitation vector, to assist with the characterization of the particular excitation and to determine the amount of spin contamination of the state. Our aim is to provide for the first time in the SF methods literature a comprehensive resource on the derivation of the formulas for $⟨{\hat{S}}^2⟩$as well as its computational implementation. After a brief discussion of the theory of the SF Bethe–Salpeter equation (BSE) and some examples further illustrating the need for calculating $⟨{\hat{S}}^2⟩$, we present the derivation for the general equation for computing $⟨{\hat{S}}^2⟩$with the eigenvectors from an SF-BSE calculation, how it is implemented in a Python script, and timing information on how this calculation scales with the size of the SF-BSE Hamiltonian. 

   more » « less
3. Do black holes remember what they are made of?

   https://doi.org/10.1088/1361-6382/ad56ed  

   Bandyopadhyay, Harshraj; Radice, David; Prakash, Aviral; Dhani, Arnab; Logoteta, Domenico; Perego, Albino; Kashyap, Rahul (June 2024, Classical and Quantum Gravity)

   Abstract We study the ringdown signal of black holes formed in prompt-collapse binary neutron star mergers. We analyze data from 47 numerical relativity simulations. We show that the $(\ell =2,m=2)$and $(\ell =2,m=1)$multipoles of the gravitational wave signal are well fitted by decaying damped exponentials, as predicted by black-hole perturbation theory. We show that the ratio of the amplitude in the two modes depends on the progenitor binary mass ratioqand reduced tidal parameter $\tilde{\mathrm{\Lambda }}$. Unfortunately, the numerical uncertainty in our data is too large to fully quantify this dependency. If confirmed, these results will enable novel tests of general relativity in the presence of matter with next-generation gravitational-wave observatories. 

   more » « less
4. Measuring neutron star radius with second and third generation gravitational wave detector networks

   https://doi.org/10.1088/1361-6382/ad828a  

   Bandopadhyay, Ananya; Kacanja, Keisi; Somasundaram, Rahul; Nitz, Alexander H; Brown, Duncan A (October 2024, Classical and Quantum Gravity)

   Abstract The next generation of ground-based interferometric gravitational wave detectors will observe mergers of black holes and neutron stars throughout cosmic time. A large number of the binary neutron star merger events will be observed with extreme high fidelity, and will provide stringent constraints on the equation of state of nuclear matter. In this paper, we investigate the systematic improvement in the measurability of the equation of state with increase in detector sensitivity by combining constraints obtained on the radius of a $1.4{\mathrm{M}}_{\odot }$neutron star from a simulated source population. Since the measurability of the equation of state depends on its stiffness, we consider a range of realistic equations of state that span the current observational constraints. We show that a single 40 km Cosmic Explorer detector can pin down the neutron star radius for a soft, medium and stiff equation of state with a precision of 10 m within a decade, whereas the current generation of ground-based detectors like the Advanced LIGO-Virgo network would take $O\left({10}^5\right)$years to do so for a soft equation of state. 

   more » « less
5. Estimating false alarm rates of sub-dominant quasi-normal modes in GW190521

   https://doi.org/10.1088/1361-6382/ad84ae  

   Capano, Collin_D; Abedi, Jahed; Kastha, Shilpa; Nitz, Alexander_H; Westerweck, Julian; Wang, Yi-Fan; Cabero, Miriam; Nielsen, Alex_B; Krishnan, Badri (November 2024, Classical and Quantum Gravity)

   Abstract A major aim of gravitational wave astronomy is to test observationally the Kerr nature of black holes. The strongest such test, with minimal additional assumptions, is provided by observations of multiple ringdown modes, also known as black hole spectroscopy. For the gravitational wave merger event GW190521, we have previously claimed the detection of two ringdown modes emitted by the remnant black hole. In this paper we provide further evidence for the detection of multiple ringdown modes from this event. We analyse the recovery of simulated gravitational wave signals designed to replicate the ringdown properties of GW190521. We quantify how often our detection statistic reports strong evidence for a sub-dominant $(\ell ,m,n)=(3,3,0)$ringdown mode, even when no such mode is present in the simulated signal. We find this only occurs with a probability ∼0.02, which is consistent with a Bayes factor of $56\pm 1$(1σuncertainty) found for GW190521. We also quantify our agnostic analysis of GW190521, in which no relationship is assumed between ringdown modes, and find that only 1 in 250 simulated signals without a $(3,3,0)$mode yields a result as significant as GW190521. Conversely, we verify that when simulated signals do have an observable $(3,3,0)$mode they consistently yield a strong evidence and significant agnostic results. We also find that constraints on deviations from the $(3,3,0)$mode on GW190521-like signals with a $(3,3,0)$mode are consistent with what was obtained from our previous analysis of GW190521. Our results support our previous conclusion that the gravitational wave signal from GW190521 contains an observable sub-dominant $(\ell ,m,n)=(3,3,0)$mode. 

   more » « less