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Transmission spectroscopy is one of the premier methods used to probe thetemperature, composition, and cloud properties of exoplanet atmospheres. Recentstudies have demonstrated that the multidimensional nature of exoplanetatmospheres -- due to non-uniformities across the day-night transition andbetween the morning and evening terminators -- can strongly influencetransmission spectra. However, the computational demands of 3D radiativetransfer techniques have precluded their usage within atmospheric retrievals.Here we introduce TRIDENT, a new 3D radiative transfer model which rapidlycomputes transmission spectra of exoplanet atmospheres with day-night,morning-evening, and vertical variations in temperature, chemical abundances,and cloud properties. We also derive a general equation for transmissionspectra, accounting for 3D atmospheres, refraction, multiple scattering,ingress/egress, grazing transits, stellar heterogeneities, and nightsidethermal emission. After introducing TRIDENT's linear algebra-based approach to3D radiative transfer, we propose new parametric prescriptions for 3Dtemperature and abundance profiles and 3D clouds. We show that multidimensionaltransmission spectra exhibit two significant observational signatures: (i)day-night composition gradients alter the relative amplitudes of absorptionfeatures; and (ii) morning-evening composition gradients distort thepeak-to-wing contrast of absorption features. Finally, we demonstrate thatthese signatures of multidimensional atmospheres incur residuals > 100 ppmcompared to 1D models, rendering them potentially detectable with JWST.TRIDENT's rapid radiative transfer, coupled with parametric multidimensionalatmospheres, unlocks the final barrier to 3D atmospheric retrievals.

TRIDENT: A Rapid 3D Radiative Transfer Model for Exoplanet Transmission Spectra