Big crunch singularities in AdS and relevant deformations of CFT s

Transcription

1 Big crunch singularities in AdS and relevant deformations of CFT s Vlad Vaganov Fields, Gravity & Strings Group Center for Theoretical Physics of the Universe Institute for Basic Science Seoul, Korea 5 th January, 2017, ICTS, USTC 5 th January, 2017, ICTS, USTC 1 / 55

2 Based on , Probing crunching AdS cosmologies , Quasinormal modes and holographic correlators in a crunching AdS geometry + ongoing.. with S. Prem Kumar (Swansea University) 5 th January, 2017, ICTS, USTC 2 / 55

3 Some previous work [hep-th] Towards a big crunch dual" Hertog,Horowitz [hep-th] Holographic description of AdS cosmologies Hertog,Horowitz On the Quantum Resolution of Cosmological Singularities using AdS/CFT" Craps, Hertog,Turok Gauge theories with time dependent couplings and their cosmological duals Trivedi, Narayan, Nampuri, Das, Awad Vacuum decay into anti de Sitter space" Maldacena AdS crunches, CFT falls and cosmological complementarity" Barbon, Rabinovici Entanglement entropy in de Sitter space" Maldacena, Pimentel Holographic signatures of cosmological singularities" Engelhardt, Hertog, Horowitz Holographic consequences of a No Transmission Principle" Engelhardt,Horowitz Cosmological singularities encoded in IR boundary correlations" Bzowski, Hertog, Schillo 5 th January, 2017, ICTS, USTC 3 / 55

4 Background and motivation Background and motivation General setup Examples from known deformations of CFT s AdS 4 /CFT 3 analytical example Holographic probes: geodesics, correlators, entanglement entropy Summary 5 th January, 2017, ICTS, USTC 4 / 55

5 Background and motivation Main theme: Toy models in holography to address (potential) resolution of cosmological singularities by string theory Secondary themes: QFT in de Sitter spacetime Nonequilibrium dynamics of strongly driven interacting QFT s 5 th January, 2017, ICTS, USTC 5 / 55

6 Background and motivation Precedent: AdS black hole singularity and behind horizon geometry probed using holography (Fidkowski/Hubeny/Kleban/Shenker 2003, Festuccia/Liu 2005, 2008). Subtle signals of black hole singularity encoded in large N thermal correlators. Is black hole singularity resolved by stringy (α ) corrections or quantum (g s ) effects? 5 th January, 2017, ICTS, USTC 6 / 55

7 Background and motivation Our focus: Spacelike cosmological curvature singularity of FRW type, big crunch. Cuts all the way across the asymptotically global AdS spacetime. Time-dependent supergravity solutions dual to a CFT deformed by a relevant operator. The field theory lives on de Sitter spacetime. There is an equivalent point of view where the field theory lives on the Einstein static universe but the relevant couplings are time-dependent and diverge at finite time. 5 th January, 2017, ICTS, USTC 7 / 55

8 Background and motivation Other toy models: CFT s on de Sitter deformed by marginal multi-trace operators (Horowitz/Hertog 2004, Craps/Hertog/Turok 2007). Dilaton deformations of AdS 5 S 5 dual to N = 4 on Minkowski with time-dependent coupling (Trivedi et al ) Kasner-AdS solutions (Horowitz-Hertog 2014). Examples in higher-spin AdS/CFT dualities. AdS black holes th January, 2017, ICTS, USTC 8 / 55

9 Background and motivation Outline: Examples and generic features of such gauge-gravity dual pairs. Potential holographic QFT signatures of bulk gravity singularity. Compare and contrast to thermal QFT/AdS black holes. Eventually hope to understand such singularities from QFT perspective. 5 th January, 2017, ICTS, USTC 9 / 55

10 Background and motivation Plan Background and motivation General setup Examples from known deformations of CFT s AdS 4 /CFT 3 analytical example Holographic probes: geodesics, correlators, entanglement entropy Summary 5 th January, 2017, ICTS, USTC 10 / 55

11 General setup Background and motivation General setup Examples from known deformations of CFT s AdS 4 /CFT 3 analytical example Holographic probes: geodesics, correlators, entanglement entropy Summary 5 th January, 2017, ICTS, USTC 11 / 55

12 General setup Euclidean picture (Horowitz/Hertog 2004,2005, Maldacena 2010) Start with Euclidean CFT on S d dual to empty Euclidean AdS ds 2 = dξ 2 + sinh 2 (ξ) dω 2 d Deform the CFT by a relevant operator (mass terms) L S d = L CFT m2 ϕ 2 5 th January, 2017, ICTS, USTC 12 / 55

13 General setup Euclidean instanton Large N dual: gravity + scalars ds 2 = dξ 2 + a 2 (ξ) dω 2 d, φ = φ(ξ), 0 ξ < Take m to be small compared to inverse sphere radius smooth origin: a ξ 0 ξ & asympt. AdS: a ξ sinh ξ O(d+1)-invariant Euclidean instanton 5 th January, 2017, ICTS, USTC 13 / 55

14 General setup Lorentzian exterior region Wick rotation θ i t + π 2 dω 2 d = dθ2 + sin 2 (θ) dω 2 d 1 dt2 + cosh 2 (t) dω 2 d 1 Deformed CFT in de Sitter (ds d ). Bulk ds-sliced asymptotically AdS exterior patch ( ) ds 2 = dξ 2 + a 2 (ξ) dt 2 + cosh 2 (t) dω 2 d 1 ξ = 0 now a horizon. 5 th January, 2017, ICTS, USTC 14 / 55

15 General setup Lorentzian interior region Can continue through the horizon into another region: ξ iσ, t χ iπ 2, a iã ( ) ds 2 dσ 2 + ã 2 (σ) dχ 2 + sinh 2 (χ) dω 2 d 1 FRW cosmology with scale factor ã and hyperbolic spatial sections. Interior patch. 5 th January, 2017, ICTS, USTC 15 / 55

16 General setup Pure AdS a = sinh ξ, ã = sin σ Exterior coordinate patch: ( ) ds 2 = dξ 2 + sinh 2 (ξ) dt 2 + cosh 2 (t) dω 2 d 1, 0 ξ < Interior coordinate patch: ( ) ds 2 = dσ 2 + sin 2 (σ) dχ 2 + sinh 2 (χ) dω 2 d 1, 0 σ π 5 th January, 2017, ICTS, USTC 16 / 55

17 General setup Pure AdS a(ξ) AdS (a = sinh[ξ]) ξ ã(σ) AdS (ã = sin[σ]) σ ξ = 0 or σ = 0: horizon σ = π: "crunch" (coordinate singularity) 5 th January, 2017, ICTS, USTC 17 / 55

18 General setup Deformed AdS with crunch a(ξ) AdS + deformation ξ ã(σ) AdS + deformation σ ξ = 0 or σ = 0: horizon σ = σ c < π: big crunch curvature singularity - unavoidable barring fine-tuning 5 th January, 2017, ICTS, USTC 18 / 55

19 General setup Penrose diagram Pure AdS Deformed AdS with crunch 5 th January, 2017, ICTS, USTC 19 / 55

20 General setup Penrose diagram Pure AdS Deformed AdS with crunch 5 th January, 2017, ICTS, USTC 19 / 55

21 General setup Coleman & de Luccia Closely related to Coleman & de Luccia(1980) false vacuum decay (e.g. Minkowski to AdS): expanding bubbles with AdS interiors AdS Deviation of scalar from AdS extremum curvature singularity (C-dL 1980). 5 th January, 2017, ICTS, USTC 20 / 55

22 General setup Conformal complementarity map Boundary ds d is conformal to R τ S d 1 (Einstein static universe = ESU). ( ) dt 2 + cosh 2 (t) dω 2 d 1 = sec2 τ dτ 2 + dω 2 d 1, < t < cosh t = 1 cos τ π 2 < τ < π 2 Can talk about theory on de Sitter or the theory on the ESU. The Lagrangians of the two theories are related as L dsd = L CFT m2 φ 2 m 2 L Rτ S d 1 = L CFT cos 2 τ φ2 Conformal complementarity map (Barbon/Rabinovici 2011,2013). 5 th January, 2017, ICTS, USTC 21 / 55

23 General setup Conformal complementarity map Bulk geometry in ds slicing: ( ) ds 2 = dξ 2 + a 2 (ξ) dt 2 + cosh 2 (t) dω 2 d 1 Bulk geometry in global slicing: ( ) cos ψ ds 2 = Λ 2 dsads 2 cos τ ( ) dsads 2 = sec2 (ψ) dτ 2 + dψ 2 + sin 2 (ψ) dω 2 d 1, 0 ψ < π 2 Λ = 1 at AdS boundary, Λ = 0 at crunch singularity. 5 th January, 2017, ICTS, USTC 22 / 55

24 General setup Aside: comparison to AdS black hole 5 th January, 2017, ICTS, USTC 23 / 55

25 General setup Comparison to AdS black hole AdS-Schw black hole AdS crunch 2 boundaries 1 boundary Singularity curved inward Static R O(d) symmetry Vacuum solution CFT in thermal state Boundary R S d 1 Singularity curved outward Time-dependent O(d, 1) symmetry Requires supergravity fields Deformation of CFT Lagrangian Boundary ds d or R τ S d 1 related by complementarity map 5 th January, 2017, ICTS, USTC 24 / 55

26 Examples from known deformations of CFT s Background and motivation General setup Examples from known deformations of CFT s AdS 4 /CFT 3 analytical example Holographic probes: geodesics, correlators, entanglement entropy Summary 5 th January, 2017, ICTS, USTC 25 / 55

27 Examples from known deformations of CFT s Examples: AdS 5 /CFT 4 (Kumar-VV (to appear)) Within N = 8 gauged supergravity in 5d N = 4 SYM + equal masses for 3 adjoint chiral multiplets (N = 1 on R 4 ): GPPZ 2-scalar truncation (Girardello/Petrini/Porrati/Zaffaroni 1999). N = 1 on S 4 : BEKOP 10-scalar truncation (Bobev/Elvang/Kol/Olson/Pufu 2016) N = 4 SYM + mass for adjoint hypermultiplet (N = 2 on R 4 ): Pilch-Warner 2-scalar truncation(pilch/warner 2000) N = 2 on S 4 : BEFP 3-scalar truncation (matching localization results) (Bobev/Elvang/Freedman/Pufu 2013) 5 th January, 2017, ICTS, USTC 26 / 55

28 Examples from known deformations of CFT s Examples: AdS 4 /CFT 3 Within N = 8 gauged supergravity in 4d M2-brane CFT (k = 1 ABJM)+ mass term ( = 1 operator): Horowitz-Hertog 1-scalar truncation (Duff/Liu 1999, Horowitz/Hertog 2004, Bzowski/Hertog/Schillo 2015) M2-brane CFT (k = 1 ABJM) + mass term ( = 1 operator): Papadimitriou-Skenderis 1-scalar truncation (Papadimitriou/Skenderis 2004) M2-brane CFT (k = 1 ABJM) + mass term preserving N = 2 SUSY on S 3 : Freedman-Pufu 3-scalar truncation (Freedman/Pufu 2013) AdS 3 /CFT 2 examples.. 5 th January, 2017, ICTS, USTC 27 / 55

29 Examples from known deformations of CFT s Construction For each truncation, S d -sliced Euclidean "ungapped" solution is constructed numerically. Start with smooth b.c. at origin and integrate out to AdS boundary. Typically find bounded mass deformation m < m crit. Continuation to ds d -sliced exterior region of the Lorentzian geometry is trivial as profiles depend only on radial coordinate. FRW interior region is obtained by integrating analytically continued equations inward from the horizon. 5 th January, 2017, ICTS, USTC 28 / 55

30 Examples from known deformations of CFT s Near-singularity behaviour (Kumar-VV (to appear)) In each case, find crunch at σ = σ c < π and ã max < 1: a pure AdS Φ0=0.3 Φ0=1.0 Φ0= σ Power law scaling as σ σ c (supergravity not reliable) ã(σ) (σ c σ) γ Generically γ = 1/d scalar potential terms are negligible. Non-generic γ also possible but depends on potential. BEFP N = 2 example (d = 4) has two branches of solution ã (σ c σ) 1/4 (generic), ã (σ c σ) 1/7 (non-generic) 5 th January, 2017, ICTS, USTC 29 / 55

31 AdS 4 /CFT 3 analytical example Background and motivation General setup Examples from known deformations of CFT s AdS 4 /CFT 3 analytical example Holographic probes: geodesics, correlators, entanglement entropy Summary 5 th January, 2017, ICTS, USTC 30 / 55

32 AdS 4 /CFT 3 analytical example AdS 4 /CFT 3 analytical example (Kumar-VV) 1-scalar truncation of N = 8 gauged supergravity in 4 dimensions. S truncated = d 4 x [ g 4 1 2κ 2 R + 1 ] 2 µφ µ Φ + V 2/3 (Φ) ( ) V 2/3 = 3 2 κ 2 L 2 cosh 3 κ Φ AdS 4 maximum at Φ = 0 with M 2 Φ = 2/L2. (in window M 2 BF < M2 < M 2 BF + 1) Two possible quantizations: Φ dual to = 2 (Dirichlet b.c.) or = 1 (Neumann b.c.) CFT operator. 5 th January, 2017, ICTS, USTC 31 / 55

33 AdS 4 /CFT 3 analytical example AdS 4 /CFT 3 analytical example Exact smooth Euclidean solution with S 3 slices (Papadimitriou 2007): ds 2 = (1 f (u) 2) [ du 2 Φ = 6 tanh 1 f, f (u) = u 2 (1 + u 2 ) + 1 u 2 dω2 3 Boundary asymptotics: Φ αu + βu α = f 0, β = f f 2 0. ] f 0 u 1 + u 2 + u 1 + f 2 0 View β as a mass deformation ( = 1 operator) of M2-brane CFT and α as its VEV (Neumann b.c.).. 5 th January, 2017, ICTS, USTC 32 / 55

34 - π 2 AdS 4 /CFT 3 analytical example Lorentzian continuation shows (analytically) FRW crunch with ã(σ) (σ c σ) 1/3 as σ σ c (generic scaling). Shape of the crunch (solid blue) and maximal expansion slice (dashed) f 0 = 0 f 0 = 0.02 f 0 = 10 π τ τ π τ π π 2 π 2 π 2 π 4 π 2 ψ π 4 π 2 ψ π 4 π 2 ψ -π 2 -π 2 -π -π -π Small deformations: crunch is almost null. Large deformations: crunch is horizontal; Penrose diagram close to a square (like BTZ). 5 th January, 2017, ICTS, USTC 33 / 55

35 Holographic probes: geodesics, correlators, entanglement entropy Background and motivation General setup Examples from known deformations of CFT s AdS 4 /CFT 3 analytical example Holographic probes: geodesics, correlators, entanglement entropy Summary 5 th January, 2017, ICTS, USTC 34 / 55

36 Holographic probes: geodesics, correlators, entanglement entropy Geodesics and correlators What QFT observables know about the crunch? Start with two-point correlation functions. First consider geodesic limit: Ψ O (x 1 ) O (x 2 ) Ψ e Sreg(x 1,x 2 ). Scaling dimension. S reg : regulated length of bulk geodesic connecting x 1 and x 2. Geodesic limit WKB limit of wave equation for a probe scalar. 5 th January, 2017, ICTS, USTC 35 / 55

37 Holographic probes: geodesics, correlators, entanglement entropy Aside: probing AdS black hole (Fidkowski/Hubeny/Kleban/Shenker 2003) 5 th January, 2017, ICTS, USTC 36 / 55

38 Holographic probes: geodesics, correlators, entanglement entropy Aside: probing AdS black hole (Fidkowski/Hubeny/Kleban/Shenker 2003) (b) 5 th January, 2017, ICTS, USTC 36 / 55

39 Holographic probes: geodesics, correlators, entanglement entropy Bouncing geodesics (Shenker et al 2003) Spacelike geodesics compute analytically continued Wightman functions in thermal CFT G 12 (t) O 1 (0) O 2 (t) HH = O 1 (0) O 1 (t iβ/2) HH for operators with 1. HH = Hartle-Hawking / thermofield double state. High-energy spacelike geodesics going from one boundary to the other bounce off the singularity. Implies singularity in correlator, as a function of complex time t, on an unphysical sheet. 5 th January, 2017, ICTS, USTC 37 / 55

40 Holographic probes: geodesics, correlators, entanglement entropy Frequency space thermal correlators (Festuccia/Liu 2005) Solve wave equation for probe scalar of mass m ϕ dual to CFT operator of dimension = d 2 + d m2 ϕ in the WKB limit ω,, u ω/ fixed. Coincides with geodesic equation upon identifying conserved "energy" of geodesic E = iu. Exponential decay of frequency-space Green s functions along imaginary axis: z c = 0 G 12 (ω) e 2i ω zc, ω i, Re(ω) = 0 dr f (r) complex tortoise coordinate of BH singularity. z c : complex Schwarzschild time it takes for a radial null geodesic to go from the AdS boundary to the singularity. z c : WKB turning point behind the horizon for large imaginary ω. 5 th January, 2017, ICTS, USTC 38 / 55

41 Holographic probes: geodesics, correlators, entanglement entropy Quasinormal modes z c determines angle made by high frequency quasinormal modes: Im(ω n ) Re(ω n ) = ± Im(z c) Re(z c ) Has been argued from a pure high frequency "eikonal" limit null rays bouncing around the BH Penrose diagram UV singularities of correlator (commutator?) in complex time asymptotic quasinormal modes (Amado-Hoyos 2008). 5 th January, 2017, ICTS, USTC 39 / 55

42 Holographic probes: geodesics, correlators, entanglement entropy Probing AdS crunches Radial bulk geodesic connects spatially antipodal points on boundary ds d. Conserved "energy" along radial geodesic: E = a(ξ) 2 ṫ. E = iu where u = ω/ is the rescaled frequency of de Sitter harmonic. Correlator can depend only on the de Sitter invariant embedding distance Z 12 = sinh t 1 sinh t 2 + cosh t 1 cosh t 2 cos (φ 1 φ 2 ) = cosh (t 1 + t 2 ) for antipodal points 1 5 th January, 2017, ICTS, USTC 40 / 55

43 Τ Holographic probes: geodesics, correlators, entanglement entropy Τ Geodesics do not probe the crunch 0 0 Π Π 2 2 Π Π Π Π 2 Geodesics connecting antipodal points exist only for E < ã max. Geodesics with E > ã max "fall" into crunch. Geodesics do not probe the crunch Imploding space pulls geodesics into crunch (Hubeny 2004) Related to crunch being curved outward Maximal expansion slice "barrier" (Engelhardt/Wall 2013) Similar observation holds for entanglement entropy (Maldacena-Pimentel 2012) 5 th January, 2017, ICTS, USTC 41 / 55

44 Holographic probes: geodesics, correlators, entanglement entropy Branch cut in frequency-space correlator (Kumar-VV) No geodesics with E > ã max corresponds to branch cut in frequency-space retarded correlator. i a max Re u Im(ω) Re(ω) Merger of discrete set of quasinormal modes. 5 th January, 2017, ICTS, USTC 42 / 55

45 Holographic probes: geodesics, correlators, entanglement entropy Late time geodesics (Kumar-VV) Late time geodesics hug the maximal FRW expansion slice ã max. Correlator in ds d (t 1 + t 2 ) O (t 1, 0) O (t 2, π) ds e ãmax(t 1+t 2 ), ( 1) large super-horizon sized separations in de Sitter (Z 12 ). Correlator in ESU frame (τ 1,2 π/2) O (τ 1, 0) O (τ 2, π) ESU ( π 2 τ (ãmax 1) ( π 1) 2 τ ) (ãmax 1) 2 ESU correlator is singular (ã max < 1) and factorises diverging condensates? 5 th January, 2017, ICTS, USTC 43 / 55

46 Holographic probes: geodesics, correlators, entanglement entropy Beyond geodesics Correlators in geodesic/wkb limit probe only as far as the maximal FRW expansion slice. To probe crunch need to go beyond geodesic limit. Solve full wave equation in the bulk. Use AdS 4 /CFT 3 analytical example. 5 th January, 2017, ICTS, USTC 44 / 55

47 Holographic probes: geodesics, correlators, entanglement entropy Wave equation in AdS 4 /CFT 3 example (Kumar-VV) Use tortoise coordinate z z = sinh 1 u, f 0 = cosech z 0, ( ) ds 2 = a 2 (z) dz 2 dt 2 + cosh 2 t dω 2 2, a 2 (z) = sinh 2 z sinh 2 (z + z 0 ) Exterior ds-sliced patch: 0 < z < and t R. Interior FRW patch: z = iπ/2 + w, t = iπ/2 + χ, with w, χ R. Crunch at z c = iπ/2 z 0 /2. 5 th January, 2017, ICTS, USTC 45 / 55

48 Holographic probes: geodesics, correlators, entanglement entropy Singular potential Radial part of wave equation of probe bulk scalar mass m ϕ in Schrödinger form ψ ω(z) + V (z) ψ ω (z) = ω 2 ψ ω (z), V (z) = m2 ϕ + 2 sinh 2 z m 2 ϕ 2 sinh 2 (z + z 0 ) 1 sinh 2 (2z + z 0 ). V WKB = m 2 a 2 regular at crunch (dashed curve). Full potential (solid curve) is singular: V 1 4 (z z c) V w 5 th January, 2017, ICTS, USTC 46 / 55

49 Holographic probes: geodesics, correlators, entanglement entropy Results Solve full wave equation in exterior ds patch with infalling b.c. at horizon. Determines frequency-space retarded correlator via Son-Starinets. Exact solution for m ϕ = 0 and arbitrary deformation f 0. Numerical determination of quasinormal poles for arbitrary m ϕ and f 0. 5 th January, 2017, ICTS, USTC 47 / 55

50 Holographic probes: geodesics, correlators, entanglement entropy Correlator for = 3 operator Focus on probes dual to scalar operators that fit spectrum of M2-brane CFT (Aharony et al 1999) mϕ 2 = 1 4 k(k 6), = k, k = 2, 3, Exact result for = 3 operator ( ) G R (ω) =3 = 2(ω 2 + 1) z ln P iω/2 1/2 [coth(2z + z 0)] z=0 f0 0 (pure ds-sliced AdS 4 ): regular (no poles). small f0 1: infinite set of quasinormal poles at ω n 2n i, n = 1, 2,... with residues scaling as f 2n infinite deformation f 0 : quasinormal poles at ω n = (2n + 1) i, n = 1, 2, th January, 2017, ICTS, USTC 48 / 55

51 Holographic probes: geodesics, correlators, entanglement entropy Infinite deformation limit In the infinite deformation limit f 0, scalar operators of all dimensions have the same quasinormal poles and correlators. Quasinormal poles at ω n = (2n + 1) i, n = 1, 2,... Same as BTZ and its higher dimensional "topological AdS BH" generalisations. Penrose diagram of AdS crunch becomes a square in infinitely deformed limit (same as BTZ). 5 th January, 2017, ICTS, USTC 49 / 55

52 Holographic probes: geodesics, correlators, entanglement entropy Quasinormal poles for = 5/2 operator For = 5/2 operator quasinormal poles move into complex plane as f 0 increases Im Ω Im Ω Im Ω f f f th January, 2017, ICTS, USTC 50 / 55

53 Holographic probes: geodesics, correlators, entanglement entropy Quasinormal poles for = 5/2 operator Im( ) Re( ) th January, 2017, ICTS, USTC 51 / 55

54 Holographic probes: geodesics, correlators, entanglement entropy Quasinormal poles for = 5/2 operator Angle made by line of poles correlated with z c Im( ) Re( ) z 0 20th 40 7th 20 1st Empirically observe f 0 Im(ω n ) Re(ω n ) 2 = 2 Im(z c ) z 0 π Re(z c ), n 1, f th January, 2017, ICTS, USTC 52 / 55

55 Holographic probes: geodesics, correlators, entanglement entropy In a nutshell Geodesics do not probe the crunch. Beyond geodesic limit, in AdS 4 /CFT 3 example, no obvious probe of crunch. Hints that shape of crunch in Penrose diagram is connected to analytic structure of quasinormal poles. Much remains to be understood: possible instabilities, simplicity of infinite deformation limit, genericity. 5 th January, 2017, ICTS, USTC 53 / 55

56 Summary Background and motivation General setup Examples from known deformations of CFT s AdS 4 /CFT 3 analytical example Holographic probes: geodesics, correlators, entanglement entropy Summary 5 th January, 2017, ICTS, USTC 54 / 55

57 Summary Summary Believed that the QFT evolution on R S d 1 is singular at τ = π/2 when the time-dependent mass m 2 / cos 2 τ diverges. Genuine sickness? Little intuition for how strongly interacting field theories with time-dependent divergent couplings behave. de Sitter QFT evolution appears to be well-defined for all times. Should be equivalent to the ESU picture, so what does the singularity mean in de Sitter? Study simple toy QFT s to get insight.. 5 th January, 2017, ICTS, USTC 55 / 55