While multiple time concept gains popularity in recent time in the similar way, like atemporal universe (1, 2, 3, 4), deeper insight of AWT is greatly welcomed here. One of the first physicists to suggest the idea of inverse time variable was P.A.Dirac for his antimatter formalism in the 1930s and Andrei Sakharov in the 1970s. S. Hawking later proposed the concept of imaginary time on background of imaginary complex numbers, used in quantum mechanics. A second temporal dimension is also seen in Penrose's twistor theory.
F-theory is a branch of string theory introduced by Cumrun Vafa, who develops mathematical descriptions, which involved a second time variable, reportedly. While it's said, many branches of F-theory involve multiple temporal (time) dimensions, Ed Witten has argued, that the second time dimension of F-theory is only a mathematical fiction used to simplify calculations. Put simply, Witten accepts additional spatial dimensions, but acceptance of at least one additional temporal dimension is less popular amongst researchers. It was established after recent discussion on Wikipedia, that F-theory is not a "two-time" theory of physics, because it has metric signature (11,1). This controversy documented illustrates the depth of confusion in contemporary physics, where clear interpretation of piles of formal equations, mechanically derived by various theorists from mutually inconsistent postulate sets remains completely unclear.
Nevertheless, from AWT perspective the situation is still quite synoptic, here. Until F-theory is claimed to be part of string theory, it's expected to follow Lorentz invariance as one of fundamental postulates of string theory. And the Lorentz invariance violates the concept of multiple radiative time arrows, so no place for additional time arrow exists in context of whatever version of string theory. Indeed, such constrain violates the concept of hidden dimensions too, because these compacted dimensions should manifests itself just by violation of Lorentz invariance, which renders string theory a fringe theory as a whole. The situation is even more complicated by fact, contemporary physics distinguishes many definitions of time, the definitions of time arrow in particular - which aren't guaranteed to be compatible mutually under various conditions. This case just illustrates the depth of general level of confusion in contemporary physics and the urgent need of robust conceptual basis based on predicate logics, i.e. in similar way, like formal math remains based so far.
The general understanding of radiative and thermodynamics time arrow in context of omnidirectional Universe expansion is, the forward time arrow leads to expansion of matter into smaller particles, including particles of radiation, i.e. bosons. This is the reason, why we cannot travel in time in larger extent, or we would evaporate or collapse. Evaporation is generally considered as a spontaneous process during which the entropy increases. But such view isn't quite general, because it's generally followed by spontaneous symmetry breaking, i.e. condensation of matter into larger groups as a result of gravitational collapse. Because physicists aren't sure, which process is "more spontaneous" here, the omnidirectional expansion of space-time from insintric perspective can be considered dual to gravitational collapse of matter, forming such space-time. In AWT the general boundary separating both these perspectives is completely observer dependent, i.e. the CMB or human scale, which is adopted to CMB scale.
Briefly speaking, all objects larger then CMB photons tends to condense by shielding effect of these photons, while the smaller ones are separated. The CMB scale corresponds the scale of solitons inside of human brains, as it brings the maximal degree of complexity, which we can interact with in common life. From human perspective every birth alternates death, the smaller organisms then CMB photons are serving like parasites or source of food for these larger ones, the droplets of rain smaller then CMB photons would evaporate in rain on behalf of larger ones due the surface dependency of vapor tension, and so on. From our observational perspective one half of universe matter would evaporate into CMB photons due the proton decay, while the rest of it will condense into black holes of the same size in the similar way, like false vacuum has separated into matter and antimatter during inflation. As we can see, we can met with dual time arrows all around us, because with respect of time dimensions our world is quite symmetrical and reversible and no prevailing arrow of entropy exists here, in fact.
From general perspective of AWT both history, both future of observable part of our Universe remains fragmentized into infinitelly many time arrows like foam membrane, which manifests by quantum uncertainty on both macroscopic scale (the past), both microscopic scale (the future). It means, time has a character of fractal foam or tree (1) in the same way, like the space foam - just dual to the later one. While such perspective is dual to atemporal Universe, we can say safely, both groups of scientists have their side of truth, here.