Research
My research has so far been focused on the holographic complexity proposals of Susskind et al., though I am broadly interested in the intersection of gravity, quantum field theory, and quantum information. My previous work, as indicated below by my publications and talks, has looked at possible links between holographic complexity and the extended black hole thermodynamics, at holographic complexity in noncommutative gauge theories, and in general properties of the ‘complexity = volume’ conjecture. My current work is largely focused on subregion complexity in holography and mixed state complexity in field theory. I am also thinking about traversable wormholes and complexity in nonlocal field theory.
Publications
Here is a list of my publications and preprints with abstracts:
E. Cáceres, J. Couch, S. Eccles and W. Fischler, Holographic Purification Complexity, 2018. [arxiv:1811.10650]
We study holographic subregion complexity, and its possible connection to purification complexity suggested recently by Agón et al. In particular, we study the conjecture that subregion complexity is the purification complexity by considering holographic purifications of a holographic mixed state. We argue that these include states with any amount of coarsegraining consistent with being a purification of the mixed state in question, corresponding holographically to different choices of the cutoff surface. We find that within the complexity = volume and complexity = spacetime volume conjectures, the subregion complexity is equal to the holographic purification complexity. For complexity = action, the subregion complexity seems to provide an upper bound on the holographic purification complexity, though we show cases where this bound is not saturated. One such example is provided by black holes with a large genus behind the horizon, which were studied by Fu et al. As such, one must conclude that these offending geometries are not holographic, that CA must be modified, or else that holographic subregion complexity in CA is not dual to the purification complexity of the corresponding reduced state.
J. Couch, S. Eccles, T. Jacobson and P. Nguyen, Holographic Complexity and Volume, JHEP 1811, 044 (2018) doi:10.1007/JHEP11(2018)044 [arxiv:1807.02186]
The previously proposed “Complexity=Volume” or CVduality is probed and developed in several directions. We show that the apparent lack of universality for large and small black holes is removed if the volume is measured in units of the maximal time from the horizon to the “final slice” (times Planck area). This also works for spinning black holes. We make use of the conserved “volume current”, associated with a foliation of spacetime by maximal volume slices, whose flux measures their volume. This flux picture suggests that there is a transfer of the complexity from the UV to the IR in holographic CFTs, which is reminiscent of thermalization behavior deduced using holography. It also naturally gives a second law for the complexity when applied at a black hole horizon. We further establish a result supporting the conjecture that a boundary foliation determines a bulk maximal foliation without gaps, establish a global inequality on maximal volumes that can be used to deduce the monotonicity of the complexification rate on a boostinvariant background, and probe CV duality in the settings of multiple quenches, spinning black holes, and RindlerAdS.
J. Couch, S. Eccles, W. Fischler and M. L. Xiao, Holographic complexity and noncommutative gauge theory, JHEP 1803, 108 (2018) doi:10.1007/JHEP03(2018)108 [arxiv:1710.07833]
We study the holographic complexity of noncommutative field theories. The fourdimensional N=4 noncommutative super YangMills theory with Moyal algebra along two of the spatial directions has a well known holographic dual as a type IIB supergravity theory with a stack of D3 branes and nontrivial NSNS B fields. We start from this example and find that the late time holographic complexity growth rate, based on the “complexity equals action” conjecture, experiences an enhancement when the noncommutativity is turned on. This enhancement saturates a new limit which is exactly 1/4 larger than the commutative value. We then attempt to give a quantum mechanics explanation of the enhancement. Finite time behavior of the complexity growth rate is also studied. Inspired by the nontrivial result, we move on to more general setup in string theory where we have a stack of Dp branes and also turn on the B field. Multiple noncommutative directions are considered in higher p cases.
J. Couch, W. Fischler and P. H. Nguyen, Noether charge, black hole volume, and complexity, JHEP 1703, 119 (2017) doi:10.1007/JHEP03(2017)119 [arxiv:1610.02038]
In this paper, we study the physical significance of the thermodynamic volumes of AdS black holes using the Noether charge formalism of Iyer and Wald. After applying this formalism to study the extended thermodynamics of a few examples, we discuss how the extended thermodynamics interacts with the recent complexity = action proposal of Brown et al. (CAduality). We, in particular, discover that their proposal for the late time rate of change of complexity has a nice decomposition in terms of thermodynamic quantities reminiscent of the Smarr relation. This decomposition strongly suggests a geometric, and via CAduality holographic, interpretation for the thermodynamic volume of an AdS black hole. We go on to discuss the role of thermodynamics in complexity = action for a number of black hole solutions, and then point out the possibility of an alternate proposal, which we dub “complexity = volume 2.0”. In this alternate proposal the complexity would be thought of as the spacetime volume of the WheelerDeWitt patch. Finally, we provide evidence that, in certain cases, our proposal for complexity is consistent with the Lloyd bound whereas CAduality is not.
Talks
Here is a list of my talks and presentations:

“Holographic Complexity and Volume,” Southwest Strings Meeting 2019, Arizona State University, Tempe, AZ (Feb 2019)

“Purification complexity in free scalar field theory,” Joint Meeting of the Texas Section of the APS, Texas Section of the AAPT, and Zone 13 of the SPS, Houston, TX (October 2018)

“Holographic Complexity,” Oklahoma State University, Stillwater OK (April 2018)

“Holographic Complexity and NonCommutative Guage Theory,” Southwest Holography Meeting 2018, University of Texas at Austin, Austin, TX (March 2018)

“Holographic Complexity and NonCommutative Guage Theory,” Joint Meeting of the Texas Section of the APS, Texas Section of the AAPT, and Zone 13 of the SPS, Richardson, TX (October 2017)
For more information about my publications, see my CV, my inSPIRE profile, or Research Gate.