arXiv subjects

Vasileios A. Letsios

Publications and source records attributed to Vasileios A. Letsios.

16 recordsLinked to original sources

arXiv2026

Sphere path integrals for fermionic gauge fields

We consider spin-$s \geq \frac{3}{2}$ complex, strictly massless fermionic gauge fields on the four-sphere, $S^4$, which is the Euclidean continuation of de Sitter spacetime, dS$_4$. For $s=\frac{5}{2}$, after briefly discussing different options for the quantisation of the theory on dS$_4$, we compute the one-loop sphere path integral. We explain how it can be expressed in terms of functional determinants, generalising previous results for $s=\frac{3}{2}$. We proceed to rewrite the result in terms of `bulk' unitary Harish-Chandra characters in the discrete series of the de Sitter isometry group, $Spin(4,1)$, and `edge' characters. We then generalise the character expression of the sphere path integral for any complex, strictly massless spin-$s\geq\frac{3}{2}$ fermionic gauge potential. Additionally, we compute the coefficient of the logarithmic divergence of the $S^4$ path integral for all spin-$s \geq \frac{3}{2}$, and we show that it is fully encoded by bulk and edge characters. We further show that at one loop no imaginary phase appears for strictly massless fermionic gauge potentials, contrary to the case of bosons. Lastly, we confirm the exact one-loop cancellation between bulk and edge contributions for the case of an infinite tower of complex massless fermions of spins $s=\frac{1}{2}, \frac{3}{2},\dots$, observed recently.

hep-th↗

arXiv2026

A discrete series gauge field at the late-time boundary of $dS_4$

We study the free Maxwell field on the planar patch of four-dimensional de Sitter spacetime ($dS_4$). We review its bulk canonical quantization in the Bunch-Davies vacuum, and we give a representation-theoretic viewpoint by studying the transformation properties of single-particle states under infinitesimal dS transformations. By taking the late-time limit, we identify two late-time operators with scaling dimensions $Δ=1$ (leading) and $Δ=2$ (subleading). We introduce CFT-inspired inner products invariant under the dS group ($SO(4,1)$) for states created by late-time operators acting on the Bunch-Davies vacuum. We explain how the unitary discrete series representations of $SO(4,1)$ associated with the photon are furnished by both operators, in contrast with the Maxwell field on $AdS$ where the $Δ=1$ operator corresponds to a non-normalizable mode. We also explain how the corresponding discrete series representations of $SO(4,1)$ split into a direct sum of representations corresponding to two helicities $+1$ and $-1$. This is achieved by taking advantage of the dS invariance of the self-dual and anti-self-dual sectors of the photon field strength. In our outlook, we draw inspiration from a recent proposal for the microscopic description of $dS_4$ higher-spin gravity where conformal gauge fields in 3 dimensions play a central role, and we investigate a possible connection of the $Δ=1$ late-time operator with a conformal spin-1 gauge field in 3 dimensions.

hep-th↗

arXiv2026

Axions on de Sitter space

We study a massless minimally coupled compact scalar, or axion, on global $D$-dimensional de Sitter space (dS$_D$). We quantise the theory canonically, determine the quantum dS charges, and find that the axion zero mode supplies a quantum-mechanical factor beyond the oscillator Fock space, $\mathcal{F}$. The full Hilbert space is $\mathcal{H}=L^2(S^1)\otimes\mathcal{F}$, with the integer quantum-mechanical momentum on $L^2(S^1)$ identified with the conserved $\mathrm{U}(1)$ shift charge. The 1-particle unitary irreducible representation (UIR) of the dS group, $\mathrm{SO}(D,1)$, captures the oscillator sector, but misses the zero mode. We find that the neutral 0-particle state is dS-invariant and normalisable. Charged 0-particle states are normalisable, but only $\mathrm{SO}(D)$ invariant. This implies that geodesic observers related by dS boosts do not agree on the particle number in a charged sector, an effect absent in QFTs equipped only with the standard Bunch-Davies vacuum. We compute field-strength Wightman 2-point functions in charged sectors and find that they are Hadamard. For non-zero charge they are not dS-invariant at finite global times, but they are asymptotically so at early and late times. We complement this analysis with a Euclidean perspective. The ordinary $D$-sphere path integral, $Z_{S^D}$, written in terms of Harish-Chandra characters, has access only to the neutral sector. Charged sectors require vertex-operator insertions, and summing over them gives a decorated sphere path integral, $\widehat{Z}_{S^D}=Z_\text{QM}\,Z_{S^D}$, that captures the entire Hilbert space, with $Z_\text{QM}$ denoting the partition function of a quantum rotor at a dimension-dependent effective temperature. Finally, in dS$_3$, we use the duality between an axion and a photon to translate our results to electromagnetism, where the axion zero mode gives rise to magnetic monopoles.

hep-th↗

arXiv2026

dS$^4$ Metamorphosis

We study the Euclidean path integral of higher spin gravity on $S^4$. Based on a one-loop analysis, we are led to a gluing formula expressing the $S^4$ path integral in terms of an underlying $S^3$ path integral. We view the three-sphere as a boundary hypersurface splitting the four-sphere into two halves. For a higher spin spectrum containing even spins only, the resulting boundary theory living on the $S^3$ cut is the $\mathrm{Sp}(N)$ invariant sector of $N\in \mathbb{Z}^+$ anti-commuting, conformally coupled free scalars, with conformal higher spin sources mediating the gluing. This boundary $\mathrm{Sp}(N)$ theory was previously shown to compute the Hartle-Hawking wavefunction at $\mathcal{I}^+$ in the higher spin dS$_4$/CFT$_3$ correspondence. In contrast to the infinite spatial volume of $\mathcal{I}^+$, here the conformal fields populate a finite size $S^3$ hypersurface of $S^4$. For theories with both bosonic and fermionic higher spin fields, the gluing formula is instead built from an $\mathcal{N}=2$ superconformal boundary field theory coupled to $U(N)$ invariant superconformal sources. Under this assumption, the leading contribution to the four-sphere partition function is $2^N$, and we observe exact cancellations at one-loop.

hep-th↗

arXiv2026

Fermionic fields of higher spin in de Sitter space

We consider fermionic fields of higher spin on a four-dimensional de Sitter background. A particular emphasis is placed on the Rarita-Schwinger spin-$\tfrac{3}{2}$ case. Both massive fields and gauge fields are considered, and their relation to the representation theory of $SO(4,1)$ is discussed. In Lorentzian signature, we study properties of the Bunch-Davies mode functions, and the late time structure of their two-point functions. For the Rarita-Schwinger gauge field, we consider a quantisation procedure based on the Minkowskian limit of the field operator. In Euclidean signature, the fields are placed on a four-sphere and the Euclidean path integral is computed at one-loop. The resulting Euclidean partition function is expressed in terms of unitary Lorentzian group characters with edge corrections. The unitary nature of the characters contrasts the lack of a conventional real action for the Rarita-Schwinger gauge field in de Sitter space. We speculate on the microscopic properties of a theory comprised of an infinite tower of interacting integer and half-integer gauge fields in de Sitter space. Along the way, we discuss a potentially interesting expression for the higher-spin path integral on the four-sphere.

hep-th↗

arXiv2026

The complete action for $\mathcal{N}=2$ de Sitter pure supergravity

Supergravity theories in de Sitter spacetime are known to be very constrained, and rather unnatural within String/M Theory. We revisit the seminal paper by Pilch, van Nieuwenhuizen and Sohnius, where the possible existence of a real Lagrangian for ${\cal N}=2$ pure supergravity in four-dimensional de Sitter spacetime was pointed out. We clarify several issues related to the non-unitarity of the theory and explicitly construct the unique, complete theory searched for long ago by the aforementioned authors. We argue that the lack of unitarity of the Lorentzian theory may be revisited in the Euclidean approach to de Sitter quantum gravity, where alternative definitions of unitarity can be introduced.

hep-th↗

arXiv2025

Unitary SUSY for the chiral graviton and chiral gravitino in de Sitter spacetime

It is commonly believed that a unitary supersymmetric quantum field theory (QFT) involving graviton and gravitino fields on fixed 4-dimensional de Sitter spacetime ($dS_4$) cannot exist due to known challenges associated with supersymmetry (SUSY) on spaces with positive cosmological constant. In this talk, we contradict this expectation by presenting a new unitary supersymmetric QFT on fixed $dS_4$ : the free supersymmetric theory of the chiral graviton and chiral gravitino fields. The theory overcomes the known obstacles to unitary global SUSY on de Sitter because the commutator between two SUSY transformations closes on the conformal algebra $so(4,2)$ rather than the de Sitter algebra $so(4,1)$. Crucially, the $so(4,2)$ symmetry is realised through unconventional conformal-like transformations. Based on arxiv:2503.04515.

hep-th↗

arXiv2025

Unitary Rigid Supersymmetry for the Chiral Graviton and Chiral Gravitino in de Sitter Spacetime

It is commonly believed that a unitary supersymmetric quantum field theory (QFT) involving graviton and gravitino fields on fixed 4-dimensional de Sitter spacetime ($dS_{4}$) cannot exist due to known challenges associated with supersymmetry (SUSY) in $dS_{4}$. In this paper, we contradict this expectation by presenting a new unitary supersymmetric QFT on $dS_{4}$: the free supersymmetric theory of the chiral graviton and chiral gravitino fields. By chiral, we mean that the corresponding field strengths are anti-self-dual, and the gauge potentials are complex, each carrying a single complex propagating degree of freedom. The global SUSY transformations are generated by the standard Dirac Killing spinors of $dS_{4}$. The theory overcomes the known obstacles to unitary global SUSY on $dS_{4}$ by closing the commutator between two SUSY transformations on $so(4,2) \oplus u(1)$ rather than the de Sitter algebra $so(4,1)$. Crucially, the $so(4,2)$ symmetry is realised through unconventional conformal-like transformations. This free theory cannot become interacting while preserving SUSY in a way that makes the spin-2 sector the true graviton sector of General Relativity, as the three-graviton coupling cannot be $u(1)$-invariant. We establish the unitarity of the free supersymmetric theory in two complementary ways. First, by studying the action of the superalgebra generators on the space of physical gravitino and graviton mode solutions. Second, by quantising the fields and explicitly constructing the complex quantum supercharges $Q_{A}$ and $Q^{A\dagger}$, we show that the trace $\sum_{A} \{ Q_{A}, Q^{A \dagger} \}$ is positive-definite.

hep-th↗

arXiv2025

Quite Discrete for a fermion

We study Discrete Series representations of $SL(2,\mathbb{R})$ with half-integer scaling dimension $Δ$. At the classical level, we show that these UIRs are realised in the space of mode solutions of spinor fields with imaginary mass parameters on a fixed two-dimensional de Sitter, dS$_{2}$, background. Upon such tuning of the mass, the field develops a fermionic shift symmetry that we characterise. We show that in the Euclidean section this manifests itself in the presence of zero-modes which preclude the definition of a Hadamard two-point function for these UIRs. We propose a Euclidean procedure to deal with the zero-modes, define a two-point function with the right singularity structure, and analyse its late-time behaviour. We end this note by proposing two interacting theories containing the fermionic discrete series in their spectrum.

hep-th↗

arXiv2024

Spinning fields on S$^d$ and dS$_d$, UIRs and Ladder operators

We construct, for spin $0,1,2$ tensor fields on S$^d$, a set of ladder operators that connect the distinct UIRs of SO$(d+1)$. This is achieved by relying on the conformal Killing vectors of S$^d$. For the case of spinning fields, the ladder operators generalize previous expressions with a compensating transformation necessary to preserve the transversality condition. We then extend the results to the Exceptional/Discrete UIRs of SO$(d,1)$, again relying on the conformal Killing vectors of de Sitter space. Our construction recovers the conventional conformal primary transformations for the scalar fields when the mass term leads to conformal coupling. A similar approach for the spin-2 field leads to the conformal-like operators found recently.

hep-th↗

arXiv2024

Unconventional conformal invariance of maximal depth partially massless fields on $dS_{4}$ and its relation to complex partially massless SUSY

Deser and Waldron have shown that maximal depth partially massless theories of higher integer spin on 4-dimensional de Sitter spacetime ($dS_{4}$) possess infinitesimal symmetries generated by the conformal Killing vectors of $dS_{4}$. However, it was later shown by Barnich, Bekaert, and Grigoriev that these theories are not invariant under the conformal algebra $so(4,2)$. To get some insight into these seemingly contradicting results we write down the full set of infinitesimal transformations generated by the 15 conformal Killing vectors of $dS_{4}$. Although the infinitesimal transformations generated by the 10 dS Killing vectors are known, the transformations generated by the 5 non-Killing conformal Killing vectors were absent from the literature, and we show that they have an `unconventional' form. In the spin-2 case, we show that the field equations and the action are invariant under the unconventional conformal transformations. For spin $s >2$, the invariance is demonstrated only at the level of the field equations. For all spins $s \geq 2$, we reproduce the result that the symmetry algebra does not close on $so(4,2)$. This is due to the appearance of higher-derivative symmetries in the commutator of two unconventional conformal transformations. Our results concerning the closure of the full algebra are inconclusive. Then we shift focus to the question of supersymmetry (SUSY) on $dS_{4}$ and our objective is twofold. First, we uncover a non-interacting supermultiplet that consists of a complex partially massless spin-2 field and a complex spin-3/2 field on $dS_{4}$. Second, we showcase the appearance of the unconventional conformal symmetries in the commutator of two SUSY transformations. Thus, this commutator closes on an algebra that is neither $so(4,1)$ nor $so(4,2)$, while its full structure is an open question. More open questions arising from our findings are also discussed.

hep-th↗

arXiv2024

New conformal-like symmetry of strictly massless fermions in four-dimensional de Sitter space

We present new infinitesimal `conformal-like' symmetries for the field equations of strictly massless spin-$s \geq 3/2$ totally symmetric tensor-spinors (i.e. gauge potentials) on 4-dimensional de Sitter spacetime ($dS_{4}$). The corresponding symmetry transformations are generated by the five closed conformal Killing vectors of $dS_{4}$, but they are not conventional conformal transformations. We show that the algebra generated by the ten de Sitter (dS) symmetries and the five conformal-like symmetries closes on the conformal-like algebra $so(4,2)$ up to gauge transformations of the gauge potentials. The transformations of the gauge-invariant field strength tensor-spinors under the conformal-like symmetries are given by the product of $γ^{5}$ times a usual infinitesimal conformal transformation of the field strengths. Furthermore, we demonstrate that the two sets of physical mode solutions, corresponding to the two helicities $\pm s$ of the strictly massless theories, form a direct sum of Unitary Irreducible Representations (UIRs) of the conformal-like algebra. We also fill a gap in the literature by explaining how these physical modes form a direct sum of Discrete Series UIRs of the dS algebra $so(4,1)$.

hep-th↗

arXiv2024

(Non-)unitarity of strictly and partially massless fermions on de Sitter space II: an explanation based on the group-theoretic properties of the spin-3/2 and spin-5/2 eigenmodes

In our previous article [Letsios 2023 J. High Energ. Phys. JHEP05(2023)015], we showed that the strictly massless spin-3/2 field, as well as the strictly and partially massless spin-5/2 fields, on $N$-dimensional ($N \geq 3 $) de Sitter spacetime ($dS_{N}$) are non-unitary unless $N=4$. The (non-)unitarity was demonstrated by simply observing that there is a (mis-)match between the representation-theoretic labels that correspond to the Unitary Irreducible Representations (UIR's) of the de Sitter (dS) algebra spin$(N,1)$ and the ones corresponding to the space of eigenmodes of the field theories. In this paper, we provide a technical representation-theoretic explanation for this fact by studying the (non-)existence of positive-definite, dS invariant scalar products for the spin-3/2 and spin-5/2 strictly/partially massless eigenmodes on $dS_{N}$ ($N \geq 3$). Our basic tool is the examination of the action of spin$(N,1)$ generators on the space of eigenmodes, leading to the following findings. For odd $N$, any dS invariant scalar product is identically zero. For even $N > 4$, any dS invariant scalar product must be indefinite. This gives rise to positive-norm and negative-norm eigenmodes that mix with each other under spin$(N,1)$ boosts. In the $N=4$ case, the positive-norm sector decouples from the negative-norm sector and each sector separately forms a UIR of spin$(4,1)$. Our analysis makes extensive use of the analytic continuation of tensor-spinor spherical harmonics on the $N$-sphere ($S^{N}$) to $dS_{N}$ and also introduces representation-theoretic techniques that are absent from the mathematical physics literature on half-odd-integer-spin fields on $dS_{N}$.

hep-th↗

arXiv2023

Conservation of all Lipkin's zilches from symmetries of the standard electromagnetic action and a hidden algebra

In 1964, Lipkin discovered the zilches, a set of conserved quantities in free electromagnetism. Among the zilches, optical chirality was identified by Tang and Cohen in 2010, serving as a measure of the handedness of light and leading to investigations into light's interactions with chiral matter. While the symmetries underlying the conservation of the zilches have been examined, the derivation of zilch conservation laws from symmetries of the standard free electromagnetic (EM) action using Noether's theorem has only been addressed in the case of optical chirality. We provide the full answer by demonstrating that the zilch symmetry transformations of the four-potential, $A_μ$, preserve the standard free EM action. We also show that the zilch symmetries belong to the enveloping algebra of a "hidden" invariance algebra of free Maxwell's equations. This "hidden" algebra is generated by familiar conformal transformations and certain "hidden" symmetry transformations of $A_μ$. Generalizations of the ``hidden'' symmetries are discussed in the presence of a material four-current, as well as in the theory of a complex Abelian gauge field. Additionally, we extend the zilch symmetries of the standard free EM action to the standard interacting action (with a non-dynamical four-current), allowing for a new derivation of the continuity equation for optical chirality in the presence of electric charges and currents. Furthermore, new continuity equations for the remaining zilches are derived.

physics.class-ph↗

arXiv2023

(Non-)unitarity of strictly and partially massless fermions on de Sitter space

We present the dictionary between the one-particle Hilbert spaces of totally symmetric tensor-spinor fields of spin $s={3}/{2}, {5}/{2}$ with any mass parameter on $D$-dimensional ($D \geq 3$) de Sitter space ($dS_{D}$) and Unitary Irreducible Representations (UIR's) of the de Sitter algebra spin$(D,1)$. Our approach is based on expressing the eigenmodes on global $dS_{D}$ in terms of eigenmodes of the Dirac operator on the ${(D-1)}$-sphere, which provides a natural way to identify the corresponding representations with known UIR's under the decomposition spin$(D,1)$ $\supset$ spin$(D)$. Remarkably, we find that four-dimensional de Sitter space plays a distinguished role in the case of the gauge-invariant theories. In particular, the strictly massless spin-3/2 field, as well as the strictly and partially massless spin-5/2 fields on $dS_{D}$, are not unitary unless $D=4$.

hep-th↗

arXiv2020

The eigenmodes for spinor quantum field theory in global de Sitter space-time

The mode solutions of the Dirac equation on $N$-dimensional de Sitter space-time ($dS_{N}$) with $(N-1)$-sphere spatial sections are obtained by analytically continuing the spinor eigenfunctions of the Dirac operator on the $N$-sphere ($S^{N}$). The analogs of flat space-time positive frequency modes are identified and a vacuum is defined. The transformation properties of the mode solutions under the de Sitter group double cover (Spin($N$,1)) are studied. We reproduce the expression for the massless spinor Wightman two-point function in closed form using the mode-sum method. By using this closed-form expression and taking advantage of the maximal symmetry of $dS_{N}$ we find an analytic expression for the spinor parallel propagator. The latter is used to construct the massive Wightman two-point function in closed form.

gr-qc↗