Complexity is simple!

Cottrell, William

doi:10.1007/jhep02(2018)039

Cited by 51 publications

(46 citation statements)

References 52 publications

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“…For some applications, the so-called 'shortcomings' of the gate definition of complexity may actually be advantageous. For other applications, we might try to modify the gate definition so that it becomes more like the complexity geometry and inherits some of its features [1][2][3][4][21][22][23][24]. But for our intended applications, the complexity geometry definition seems superior.…”

Section: Gate Complexitymentioning

confidence: 99%

Complexity geometry of a single qubit

Brown

Susskind

2019

Phys. Rev. D

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The computational complexity of a quantum state quantifies how hard it is to make. 'Complexity geometry', first proposed by Nielsen, is an approach to defining computational complexity using the tools of differential geometry. Here we demonstrate many of the attractive features of complexity geometry using the example of a single qubit, which turns out to be rich enough to be illustrative but simple enough to be illuminating.

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Section: Gate Complexitymentioning

confidence: 99%

Complexity geometry of a single qubit

Brown

Susskind

2019

Phys. Rev. D

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“…The weak gravity conjecture (WGC) was originally motivated by a semi-classical black hole decay argument, hinting at a more profound reason behind it than simply circumstantial evidence from special (perturbative) points in the moduli space of string theory. A significant amount of effort has been put in the task of providing convincing arguments for or even an explicit derivation of the weak gravity conjecture, without using an explicit embedding into string theory [9][10][11][12][13][14][15][16][17]. Over the time it was realized that the different swampland conjectures are not unrelated, but rather form a tight web with many interrelations [4,8,[18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Swampland variations on a theme by KKLT

Blumenhagen

Klaewer

Schlechter

2019

J. High Energ. Phys.

187

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The KKLT scenario in a warped throat, if consistent, provides a concrete counterexample to both the AdS scale separation and the dS swampland conjectures. First, we define and analyze the relevant effective field theory for the conifold modulus and the overall Kähler modulus that both have exponentially small masses. The scalar potential still admits KKLT-like AdS and dS minima. Second, we critically analyze the reliability of the employed Wilsonian effective action by evaluating the masses of light modes localized in the warped throat. The resulting mass spectrum is discussed with respect to the swampland distance conjecture. We find the recently observed emergent nature of the latter not only at large distance points but also at the conifold point motivating a general extension of it. In this respect, KKLT and trans-Planckian field distance are on equal footing. It is pointed out that the reliability of the KKLT minimum will depend on how this emergent behavior is interpreted.

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“…Of course, the point is that we now have the tools of holography at our disposal -we can attack the problem from two sides, the bulk and the dual field theory description. A similar approach was followed in [78,95] and in [96], where we tried to relate the WGC to Lloyd's bound for the C = A proposal for holographic complexity. See [97] for a thorough analysis of WGC bounds in AdS space.…”

Section: Introductionmentioning

confidence: 99%

A holographic derivation of the weak gravity conjecture

Montero

2019

J. High Energ. Phys.

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The Weak Gravity Conjecture (WGC) demands the existence of superextremal particles in any consistent quantum theory of gravity. The standard lore is that these particles are introduced to ensure that extremal black holes are either unstable or marginally stable, but it is not clear what is wrong if this doesn't happen. This note shows that, for a generic Einstein quantum theory of gravity in AdS, exactly stability of extremal black branes is in tension with rigorously proven quantum information theorems about entanglement entropy. Avoiding the contradiction leads to a nonperturbative version of the WGC, which reduces to the usual statement at weak coupling. The argument is general, and it does not rely on either supersymmetry or a particular UV completion, assuming only the validity of Einsteinian gravity, effective field theory, and holography. The pathology is related to the development of an infinite throat in the near-horizon region of the extremal solutions, which suggests a connection to the ER=EPR proposal.So far, there is a healthy number of proposed Swampland criteria. Among these, one may count the Swampland Distance Conjecture [4], the Chern-Simons Pandemic [5], or the recent conjecture on the scalar potential [6,7], which leads to the dramatic (and debated [8-30]) conclusion that there are no de Sitter vacua in string theory (this has been suspected long before [6,31]; see [32] for a thorough review of the stringy arguments against de Sitter,and [33] for arguments supporting the conjecture). Most of these remain conjectures primarily supported by a large variety of stringy examples.There are few cases where more solid arguments can be given: Absence of continuous spin representations can be rigorously proven in string theory [34], and there are also heuristic arguments supporting it [35]. The absence of global symmetries in quantum gravity [36][37][38][39] is very well supported by both heuristics [40], worldsheet [41] and holographic [42-45] arguments.One of the most far-reaching Swampland constraints is the Weak Gravity Conjecture (WGC) [46]. In its original form, it says that in any effective field theory with gauge fields consistently coupled to Einsteinian gravity, there should be a state whose charge-to-mass ratio is equal to or larger than that of an extremal black hole. This has the effect of rendering the black hole unstable via Schwinger pair production of charged particles. This is only the mildest form of the conjecture. There are several more refined and constraining versions, such as a version applying to axions and other p-form fields, the Convex Hull Condition [47], Lattice and Tower WGC [48, 49], scalar versions of the conjecture [50-53] (leading to a connection to the Distance Conjecture and emergence [54-57]), and a variant leading to the instability of nonsupersymmetric AdS space [58, 59] (and to proposed constraints on the Standard Model [60-63]).Variants of the WGC have also been argued to constrain axion models of inflation or relaxation [48,58,[64][65][66][67][68][69][70][71][7...

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Complexity is simple!

Cited by 51 publications

References 52 publications

Complexity geometry of a single qubit

Complexity geometry of a single qubit

Swampland variations on a theme by KKLT

A holographic derivation of the weak gravity conjecture

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