Abstract:We evaluate the full time dependence of holographic complexity in various eternal black hole backgrounds using both the complexity=action (CA) and the complexity=volume (CV) conjectures. We conclude using the CV conjecture that the rate of change of complexity is a monotonically increasing function of time, which saturates from below to a positive constant in the late time limit. Using the CA conjecture for uncharged black holes, the holographic complexity remains constant for an initial period, then briefly decreases but quickly begins to increase. As observed previously, at late times, the rate of growth of the complexity approaches a constant, which may be associated with Lloyd's bound on the rate of computation. However, we find that this late time limit is approached from above, thus violating the bound. For either conjecture, we find that the late time limit for the rate of change of complexity is saturated at times of the order of the inverse temperature. Adding a charge to the eternal black holes washes out the early time behaviour, i.e. complexity immediately begins increasing with sufficient charge, but the late time behaviour is essentially the same as in the neutral case. We also evaluate the complexity of formation for charged black holes and find that it is divergent for extremal black holes, implying that the states at finite chemical potential and zero temperature are infinitely more complex than their finite temperature counterparts.

We study two recent conjectures for holographic complexity: the complexity=action conjecture and the complexity=volume conjecture. In particular, we examine the structure of the UV divergences appearing in these quantities, and show that the coefficients can be written as local integrals of geometric quantities in the boundary. We also consider extending these conjectures to evaluate the complexity of the mixed state produced by reducing the pure global state to a specific subregion of the boundary time slice. The UV divergences in this subregion complexity have a similar geometric structure, but there are also new divergences associated with the geometry of the surface enclosing the boundary region of interest. We discuss possible implications arising from the geometric nature of these UV divergences.

Recently, the ATLAS and CMS collaborations have announced the discovery of a 125 GeV particle, commensurable with the Higgs boson. We analyze the 2011 and 2012 LHC and Tevatron Higgs data in the context of simplified new physics models, paying close attention to models which can enhance the diphoton rate and allow for a natural weak-scale theory. Combining the available LHC and Tevatron data in the h → ZZ * → 4l, h → W W * → lνlν, h → γγ, hjj → γγjj and hV → bbV channels, we derive constraints on an effective low-energy theory of the Higgs boson. We map several simplified scenarios to the effective theory, capturing numerous new physics models such as supersymmetry, composite Higgs, dilaton. We further study models with extended Higgs sectors which can naturally enhance the diphoton rate. We find that the current Higgs data are consistent with the Standard Model Higgs boson and, consequently, the parameter space in all models which go beyond the Standard Model is highly constrained.