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We construct generating functions for operators dual to systems of giant gravitons with open strings attached. These operators have a bare dimension of order $N$ so that the usual methods used to solve the planar limit are not applicable. The generating functions are given as integrals over auxiliary variables, which implement symmetrization and antisymmetrization of the indices of the fields from which the operator is composed. Operators of a good scaling dimension (eigenstates of the dilatation operator) are known as Gauss graph operators. Our generating functions give a simple construction of the Gauss graph operators which were previously obtained using a Fourier transform on a double coset. The new description provides a natural starting point for a systematic ${1\over N}$ expansion for these operators as well as the action of the dilatation operator on them, in terms of a saddle point evaluation of their integral representation., Comment: 71+1 pages; Version 2 is JHEP version

We initiate a systematic study of fracton physics within the geometric framework of Double Field Theory. We ascribe the immobility and large degeneracy of the former to the non-Riemannian backgrounds of the latter, in terms of generalised geodesics and infinite-dimensional isometries. A doubled pure Yang-Mills or Maxwell theory reduces to an ordinary one coupled to a strain tensor of elasticity theory, and thus rather remarkably provides a unifying description of photons and phonons. Upon a general Double Field Theory background, which consists of Riemannian and non-Riemannian subspaces, the dual photon-phonon pair becomes fractonic over the non-Riemannian subspace. When the elasticity displacement vector condenses, minimally coupled charged particles acquire an effective mass even in the purely Riemannian case, yielding predictions for polaron physics and time crystals. Furthermore, the immobility of neutral particles along the non-Riemannian directions is lifted to a saturation velocity for charged particles. Utilising the differential geometry of Double Field Theory we also present curved spacetime extensions which exhibit general covariance., Comment: v3) Published version. Title changed from "Fractons, geometrically" to current title; minor revisions. v2) 12 pages + appendix + references = 17 pages. Revised and expanded version: includes extensions to curved spacetime, predictions for polaron mass and time crystals, further clarifying remarks and details, and additional references. v1) 5 pages + supplemental material + references = 10 pages

We define circuits given by unitary representations of Lorentzian conformal field theory in 3 and 4 dimensions. Our circuits start from a spinning primary state, allowing us to generalize formulas for the circuit complexity obtained from circuits starting from scalar primary states. These results are nicely reproduced in terms of the geometry of coadjoint orbits of the conformal group. In contrast to the complexity geometry obtained from scalar primary states, the geometry is more complicated and the existence of conjugate points, signaling the saturation of complexity, remains open., Comment: 30+1 pages; v2: refs added

We initiate a systematic study of fracton physics within the geometric framework of Double Field Theory. We ascribe the immobility and large degeneracy of the former to the non-Riemannian backgrounds of the latter, in terms of generalised geodesics and infinite-dimensional isometries. A doubled pure Yang-Mills or Maxwell theory reduces to an ordinary one coupled to a strain tensor of elasticity theory, and thus rather remarkably provides a unifying description of photons and phonons. Upon a general Double Field Theory background, which consists of Riemannian and non-Riemannian subspaces, the dual photon-phonon pair becomes fractonic over the non-Riemannian subspace. When the elasticity displacement vector condenses, minimally coupled charged particles acquire an effective mass even in the purely Riemannian case, yielding predictions for polaron physics and time crystals. Furthermore, the immobility of neutral particles along the non-Riemannian directions is lifted to a saturation velocity for charged particles. Utilising the differential geometry of Double Field Theory we also present curved spacetime extensions which exhibit general covariance., Comment: v3) Published version. Title changed from "Fractons, geometrically" to current title; minor revisions. v2) 12 pages + appendix + references = 17 pages. Revised and expanded version: includes extensions to curved spacetime, predictions for polaron mass and time crystals, further clarifying remarks and details, and additional references. v1) 5 pages + supplemental material + references = 10 pages

We define circuits given by unitary representations of Lorentzian conformal field theory in 3 and 4 dimensions. Our circuits start from a spinning primary state, allowing us to generalize formulas for the circuit complexity obtained from circuits starting from scalar primary states. These results are nicely reproduced in terms of the geometry of coadjoint orbits of the conformal group. In contrast to the complexity geometry obtained from scalar primary states, the geometry is more complicated and the existence of conjugate points, signaling the saturation of complexity, remains open., Comment: 30+1 pages; v2: refs added

We study the spectrum of anomalous dimensions of operators dual to giant graviton branes. The operators considered belong to the su$(2|3)$ sector of ${\cal N}=4$ super Yang-Mills theory, have a bare dimension $\sim N$ and are a linear combination of restricted Schur polynomials with $p\sim O(1)$ long rows or columns. In the same way that the operator mixing problem in the planar limit can be mapped to an integrable spin chain, we find that our problem maps to particles hopping on a lattice. The detailed form of the model is in precise agreement with the expected world volume dynamics of $p$ giant graviton branes, which is a U$(p)$ Yang-Mills theory. The lattice model we find has a number of noteworthy features. It is a lattice model with all-to-all sites interactions and quenched disorder., Comment: 34 pages

The state space of excited giant graviton brane systems is given by the Gauss graph operators. After restricting to the $su(2|3)$ sector of the theory, we consider this state space. Our main result is the decomposition of this state space into irreducible representations of the $su(2|2)\ltimes\mathbb{R}$ global symmetry. Excitations of the giant graviton branes are charged under a central extension of the global symmetry. The central extension generates gauge transformations so that the action of the central extension vanishes on physical states. Indeed, we explicitly demonstrate that the central charge is set to zero by the Gauss Law of the brane world volume gauge theory., Comment: 35+1 pages

The state space of excited giant graviton brane systems is given by the Gauss graph operators. After restricting to the $su(2|3)$ sector of the theory, we consider this state space. Our main result is the decomposition of this state space into irreducible representations of the $su(2|2)\ltimes\mathbb{R}$ global symmetry. Excitations of the giant graviton branes are charged under a central extension of the global symmetry. The central extension generates gauge transformations so that the action of the central extension vanishes on physical states. Indeed, we explicitly demonstrate that the central charge is set to zero by the Gauss Law of the brane world volume gauge theory., Comment: 35+1 pages

Efficient and powerful approaches to the computation of correlation functions involving determinant, sub-determinant and permanent operators, as well as traces, have recently been developed in the setting of ${\cal N}=4$ super Yang-Mills theory. In this article we show that they can be extended to ABJM and ABJ theory. After making use of a novel identity which follows from character orthogonality, an integral representation of certain projection operators used to define Schur polynomials is given. This integral representation provides an effective description of the correlation functions of interest. The resulting effective descriptions have ${1\over N}$ as the loop counting parameter, strongly suggesting their relevance for holography., Comment: 1+22 pages, 3 Figures

A new approach to the computation of correlation functions involving two determinant operators as well as one non-protected single trace operator has recently been developed by Jiang, Komatsu and Vescovi. This correlation function provides the holographic description of the absorption of a closed string by a giant graviton. The analysis has a natural interpretation in the framework of group representation theory, which admits a generalization to general Schur polynomials and restricted Schur polynomials. This generalizes the holographic description to any giant or dual giant gravitons which carry more than one angular momentum on the sphere. For a restricted Schur polynomial labeled by a column with $N$ boxes (dual to a maximal giant graviton) we find evidence in favor of integrability., Comment: 50 pages, 4 figures. v2: refs added

We study the structure constant of a single trace operator and two determinant operators in ${\cal N}=4$ super Yang-Mills theory. Holographically such a quantity corresponds to the interaction vertex between a closed string and two open strings attached to the spherical $D$-branes. Relying on diagrammatic intuition, we conjecture that the structure constant at the finite coupling is nicely written by the hexagon form factors. Precisely we need to prepare two hexagon twist operators and appropriately glue edges together by integrating mirror particles contributions and by contracting boundary states. The gluing generates the worldsheet for a closed string and two open strings attached to the $D$-branes. At the weak coupling, the asymptotic expression simply reduces to sum over all possible partitions not only for the edge related to the closed string but also for the edges representing the half of the open string together with reflection effects for the opposite open string edges. We test the conjecture by directly computing various tree level structure constants. The result is nicely matched with our conjecture., Comment: 20 pages, 2 figures

Efficient and powerful approaches to the computation of correlation functions involving determinant, sub-determinant and permanent operators, as well as traces, have recently been developed in the setting of ${\cal N}=4$ super Yang-Mills theory. In this article we show that they can be extended to ABJM and ABJ theory. After making use of a novel identity which follows from character orthogonality, an integral representation of certain projection operators used to define Schur polynomials is given. This integral representation provides an effective description of the correlation functions of interest. The resulting effective descriptions have ${1\over N}$ as the loop counting parameter, strongly suggesting their relevance for holography., Comment: 1+22 pages, 3 Figures

A new approach to the computation of correlation functions involving two determinant operators as well as one non-protected single trace operator has recently been developed by Jiang, Komatsu and Vescovi. This correlation function provides the holographic description of the absorption of a closed string by a giant graviton. The analysis has a natural interpretation in the framework of group representation theory, which admits a generalization to general Schur polynomials and restricted Schur polynomials. This generalizes the holographic description to any giant or dual giant gravitons which carry more than one angular momentum on the sphere. For a restricted Schur polynomial labeled by a column with $N$ boxes (dual to a maximal giant graviton) we find evidence in favor of integrability., Comment: 50 pages, 4 figures. v2: refs added

We study the structure constant of a single trace operator and two determinant operators in ${\cal N}=4$ super Yang-Mills theory. Holographically such a quantity corresponds to the interaction vertex between a closed string and two open strings attached to the spherical $D$-branes. Relying on diagrammatic intuition, we conjecture that the structure constant at the finite coupling is nicely written by the hexagon form factors. Precisely we need to prepare two hexagon twist operators and appropriately glue edges together by integrating mirror particles contributions and by contracting boundary states. The gluing generates the worldsheet for a closed string and two open strings attached to the $D$-branes. At the weak coupling, the asymptotic expression simply reduces to sum over all possible partitions not only for the edge related to the closed string but also for the edges representing the half of the open string together with reflection effects for the opposite open string edges. We test the conjecture by directly computing various tree level structure constants. The result is nicely matched with our conjecture., Comment: 20 pages, 2 figures

We study semiclassical string solutions that live on white regions of the LLM plane for a generic LLM geometry. These string excitations are labelled by conserved charges E, J and S and are thus holographically dual to operators in the SL(2) sector of N = 4 super-Yang Mills made up of covariant derivatives acting on complex scalar fields Z. On the other hand, the LLM geometry itself is dual to an operator consisting of O(N^2) Z-fields so that the operators dual to our solutions, containing both the stringy excitation and background, are non-planar. In an appropriate short string limit we argue that the string solution we find should be dual to a localised SL(2) excitation in the gauge theory language. This allows us to perform a non-trivial check of the recent proposal that the dynamics of localised excitations should be identical, up to a rescaling of the 't Hooft coupling, to the dynamics of those same excitations in the AdS5xS5 background, Comment: 10+3 pages

We consider operators in ${\cal N}=4$ super Yang-Mills theory dual to closed string states propagating on a class of LLM geometries. The LLM geometries we consider are specified by a boundary condition that is a set of black rings on the LLM plane. When projected to the LLM plane, the closed strings are polygons with all corners lying on the outer edge of a single ring. The large $N$ limit of correlators of these operators receives contributions from non-planar diagrams even for the leading large $N$ dynamics. Our interest in these fluctuations is because a previous weak coupling analysis argues that the net effect of summing the huge set of non-planar diagrams, is a simple rescaling of the 't Hooft coupling. We carry out some nontrivial checks of this proposal. Using the $su(2|2)^2$ symmetry we determine the two magnon $S$-matrix and demonstrate that it agrees, up to two loops, with a weak coupling computation performed in the CFT. We also compute the first finite size corrections to both the magnon and the dyonic magnon by constructing solutions to the Nambu-Goto action that carry finite angular momentum. These finite size computations constitute a strong coupling confirmation of the proposal., Comment: v2 matches published version

We study semiclassical string solutions that live on white regions of the LLM plane for a generic LLM geometry. These string excitations are labelled by conserved charges E, J and S and are thus holographically dual to operators in the SL(2) sector of N = 4 super-Yang Mills made up of covariant derivatives acting on complex scalar fields Z. On the other hand, the LLM geometry itself is dual to an operator consisting of O(N^2) Z-fields so that the operators dual to our solutions, containing both the stringy excitation and background, are non-planar. In an appropriate short string limit we argue that the string solution we find should be dual to a localised SL(2) excitation in the gauge theory language. This allows us to perform a non-trivial check of the recent proposal that the dynamics of localised excitations should be identical, up to a rescaling of the 't Hooft coupling, to the dynamics of those same excitations in the AdS5xS5 background, Comment: 10+3 pages

We consider operators in ${\cal N}=4$ super Yang-Mills theory dual to closed string states propagating on a class of LLM geometries. The LLM geometries we consider are specified by a boundary condition that is a set of black rings on the LLM plane. When projected to the LLM plane, the closed strings are polygons with all corners lying on the outer edge of a single ring. The large $N$ limit of correlators of these operators receives contributions from non-planar diagrams even for the leading large $N$ dynamics. Our interest in these fluctuations is because a previous weak coupling analysis argues that the net effect of summing the huge set of non-planar diagrams, is a simple rescaling of the 't Hooft coupling. We carry out some nontrivial checks of this proposal. Using the $su(2|2)^2$ symmetry we determine the two magnon $S$-matrix and demonstrate that it agrees, up to two loops, with a weak coupling computation performed in the CFT. We also compute the first finite size corrections to both the magnon and the dyonic magnon by constructing solutions to the Nambu-Goto action that carry finite angular momentum. These finite size computations constitute a strong coupling confirmation of the proposal., Comment: v2 matches published version

We study three-point functions of operators on the $1/2$ BPS Wilson loop in planar $\mathcal{N}=4$ super Yang-Mills theory. The operators we consider are "defect changing operators", which change the scalar coupled to the Wilson loop. We first perform the computation at two loops in general set-ups, and then study a special scaling limit called the ladders limit, in which the spectrum is known to be described by a quantum mechanics with the SL(2,$\mathbb{R}$) symmetry. In this limit, we resum the Feynman diagrams using the Schwinger-Dyson equation and determine the structure constants at all order in the rescaled coupling constant. Besides providing an interesting solvable example of defect conformal field theories, our result gives invaluable data for the integrability-based approach to the structure constants., Comment: 31 pages + appendices; v2 References added

We study structure constants of local operators inserted on the Wilson loop in ${\cal N}=4$ super Yang-Mills theory. We compute the structure constants in the SU(2) sector at tree level using the correspondence between operators on the Wilson loop and the open spin chain. The results are interpreted as the summation over all possible ways of changing the signs of magnon momenta in the hexagon form factors. This is consistent with a holographic description of the correlator as the cubic open string vertex, which consists of one hexagonal patch and three boundaries. We then conjecture that a similar expression should hold also at finite coupling., Comment: 38 pages; v3: JHEP published version

We make an attempt to map the integrable boundary conditions for 2 dimensional non-linear O(N) $\sigma$-models. We do it at various levels: classically, by demanding the existence of infinitely many conserved local charges and also by constructing the double row transfer matrix from the Lax connection, which leads to the spectral curve formulation of the problem; at the quantum level, we describe the solutions of the boundary Yang-Baxter equation and derive the Bethe-Yang equations. We then show how to connect the thermodynamic limit of the boundary Bethe-Yang equations to the spectral curve., Comment: Dedicated to the memory of Petr Kulish, 31 pages, 1 figure, v2: conformality and integrability of the boundary conditions are distinguished

We study three-point functions of operators on the $1/2$ BPS Wilson loop in planar $\mathcal{N}=4$ super Yang-Mills theory. The operators we consider are "defect changing operators", which change the scalar coupled to the Wilson loop. We first perform the computation at two loops in general set-ups, and then study a special scaling limit called the ladders limit, in which the spectrum is known to be described by a quantum mechanics with the SL(2,$\mathbb{R}$) symmetry. In this limit, we resum the Feynman diagrams using the Schwinger-Dyson equation and determine the structure constants at all order in the rescaled coupling constant. Besides providing an interesting solvable example of defect conformal field theories, our result gives invaluable data for the integrability-based approach to the structure constants., Comment: 31 pages + appendices; v2 References added

We make an attempt to map the integrable boundary conditions for 2 dimensional non-linear O(N) $\sigma$-models. We do it at various levels: classically, by demanding the existence of infinitely many conserved local charges and also by constructing the double row transfer matrix from the Lax connection, which leads to the spectral curve formulation of the problem; at the quantum level, we describe the solutions of the boundary Yang-Baxter equation and derive the Bethe-Yang equations. We then show how to connect the thermodynamic limit of the boundary Bethe-Yang equations to the spectral curve., Comment: Dedicated to the memory of Petr Kulish, 31 pages, 1 figure, v2: conformality and integrability of the boundary conditions are distinguished

We study structure constants of local operators inserted on the Wilson loop in ${\cal N}=4$ super Yang-Mills theory. We compute the structure constants in the SU(2) sector at tree level using the correspondence between operators on the Wilson loop and the open spin chain. The results are interpreted as the summation over all possible ways of changing the signs of magnon momenta in the hexagon form factors. This is consistent with a holographic description of the correlator as the cubic open string vertex, which consists of one hexagonal patch and three boundaries. We then conjecture that a similar expression should hold also at finite coupling., Comment: 38 pages; v3: JHEP published version

The exact slope function was first proposed in $SL(2)$ sector and generalized to $SU(2)$ sector later. In this note, we consider the slope function in $SU(1|1)$ sector of ${\cal N}=4$ SYM. We derive the quantity through the method invented by N. Gromov and discuss about its validity. Further, we give comments on the slope function in deformed SYM., Comment: 9 pages, no figure

The exact slope function was first proposed in $SL(2)$ sector and generalized to $SU(2)$ sector later. In this note, we consider the slope function in $SU(1|1)$ sector of ${\cal N}=4$ SYM. We derive the quantity through the method invented by N. Gromov and discuss about its validity. Further, we give comments on the slope function in deformed SYM., Comment: 9 pages, no figure

We construct the spectral curve of gamma-deformed AdS/CFT from the strong coupling scaling limit of the T-system. As we interpret the twisted T-functions in the classical limit as characters of the highest weight representations of the psu(2,2|4) symmetry group, we compute the twisted quasimomenta which characterize classical integrability and analyze their analytic and asymptotic properties. These twisted quasimomenta are compared to Beisert-Roiban Bethe ansatz equations and classical string solutions., Comment: 14 pages; v2 references added and typos corrected

We construct the spectral curve of gamma-deformed AdS/CFT from the strong coupling scaling limit of the T-system. As we interpret the twisted T-functions in the classical limit as characters of the highest weight representations of the psu(2,2|4) symmetry group, we compute the twisted quasimomenta which characterize classical integrability and analyze their analytic and asymptotic properties. These twisted quasimomenta are compared to Beisert-Roiban Bethe ansatz equations and classical string solutions., Comment: 14 pages; v2 references added and typos corrected

The concept of spectral curve is generalized to open strings in AdS/CFT with integrability preserving boundary conditions. Our definition is based on the logarithms of the eigenvalues of the open monodromy matrix and makes possible to determine all the analytic, symmetry and asymptotic properties of the quasimomenta. We work out the details of the whole construction for the Y = 0 brane boundary condition. The quasimomenta of open circular strings are explicitly calculated. We use the asymptotic solutions of the Y -system and the boundary Bethe Ansatz equations to recover the spectral curve in the strong coupling scaling limit. Using the curve the quasiclassical fluctuations of some open string solutions are also studied., Comment: 34 pages, 2 figures; v3: typos corrected, sect.2.2 improved

The concept of spectral curve is generalized to open strings in AdS/CFT with integrability preserving boundary conditions. Our definition is based on the logarithms of the eigenvalues of the open monodromy matrix and makes possible to determine all the analytic, symmetry and asymptotic properties of the quasimomenta. We work out the details of the whole construction for the Y = 0 brane boundary condition. The quasimomenta of open circular strings are explicitly calculated. We use the asymptotic solutions of the Y -system and the boundary Bethe Ansatz equations to recover the spectral curve in the strong coupling scaling limit. Using the curve the quasiclassical fluctuations of some open string solutions are also studied., Comment: 34 pages, 2 figures; v3: typos corrected, sect.2.2 improved

We compute perturbative worldsheet S-matrix of beta-deformed AdS/CFT in the strong and weak `t Hooft coupling limit to compare with exact S-matrix. For the purpose we take near BMN limit of TsT-transformed AdS_5 x S^5 with the twisted boundary condition and compute the S-matrix on worldsheet using light-cone gauge fixed Lagrangian. For the weak coupling side, we compute the S-matrix in the SU(3) sector by applying coordinate Bethe ansatz method to the one-loop dilatation operator obtained from the deformed super Yang-Mills theory. These analysis support the conjectured exact S-matrix in the leading order for both sides of beta-deformed AdS/CFT along with appropriate twisted boundary conditions., Comment: 12 pages

In the presence of uniform D-instanton charges, quarks can be confined although gluons are not, because baryon vertices are allowed due to the net repulsive force on the on the probe D-branes. Since there is no scale in the geometry itself apart from the horizon size, there is no Hawking-Page transition. As a consequence, the D7 brane embedding can encode the effect of the the finite temperature as well as finite baryon density even for low temperature. The probe D-brane embedding, however, undergoes a chiral phase transition according to the temperature and density parameter. We studied such phase transitions and calculated the constituent quark mass, chiral condensation and the binding energy of baryons as function of the density. The baryon vertex melting is identified as the quark deconfinement. We draw phase diagram according to these transitions., Comment: 33 pages, 21 figures. arXiv admin note: extreme text overlap with arXiv:1105.2872

We compute both classical and quantum finite-size corrections at leading order in the strong coupling limit for the (dyonic) giant magnon in the Lunin-Maldacena background. Based on the exact S-martix conjectured for the deformed theory, we generalize the Luscher formula to include twisted boundary conditions and show that the results match with those derived both by finite-size classical solutions of the giant magnon and by algebraic curve analysis., Comment: 13 pages

We compute perturbative worldsheet S-matrix of beta-deformed AdS/CFT in the strong and weak `t Hooft coupling limit to compare with exact S-matrix. For the purpose we take near BMN limit of TsT-transformed AdS_5 x S^5 with the twisted boundary condition and compute the S-matrix on worldsheet using light-cone gauge fixed Lagrangian. For the weak coupling side, we compute the S-matrix in the SU(3) sector by applying coordinate Bethe ansatz method to the one-loop dilatation operator obtained from the deformed super Yang-Mills theory. These analysis support the conjectured exact S-matrix in the leading order for both sides of beta-deformed AdS/CFT along with appropriate twisted boundary conditions., Comment: 12 pages

In the presence of uniform D-instanton charges, quarks can be confined although gluons are not, because baryon vertices are allowed due to the net repulsive force on the on the probe D-branes. Since there is no scale in the geometry itself apart from the horizon size, there is no Hawking-Page transition. As a consequence, the D7 brane embedding can encode the effect of the the finite temperature as well as finite baryon density even for low temperature. The probe D-brane embedding, however, undergoes a chiral phase transition according to the temperature and density parameter. We studied such phase transitions and calculated the constituent quark mass, chiral condensation and the binding energy of baryons as function of the density. The baryon vertex melting is identified as the quark deconfinement. We draw phase diagram according to these transitions., Comment: 33 pages, 21 figures. arXiv admin note: extreme text overlap with arXiv:1105.2872

We compute both classical and quantum finite-size corrections at leading order in the strong coupling limit for the (dyonic) giant magnon in the Lunin-Maldacena background. Based on the exact S-martix conjectured for the deformed theory, we generalize the Luscher formula to include twisted boundary conditions and show that the results match with those derived both by finite-size classical solutions of the giant magnon and by algebraic curve analysis., Comment: 13 pages

We study the phase diagram of a holographic QCD using the probe D7 brane in black D3 geometry with finite D-instanton charge. Due to quasi-confining nature of the geometry, baryon vertex can exist outside the horizon so that we can find D7 brane embeddings with finite baryon density and finite chiral condensation as well as an embedding where only quarks are possible but chiral condensation can be zero or non-zero. We study the phase transition and phase diagram between these phases. We also calculated constituent quark mass and binding energy of baryons as fucntion of the density., Comment: Withdrawn due to the inaccurate title. Replaced by arXive:1203.4883, "Holographic Instanton Liquid and chiral transition."

We study the phase diagram of a holographic QCD using the probe D7 brane in black D3 geometry with finite D-instanton charge. Due to quasi-confining nature of the geometry, baryon vertex can exist outside the horizon so that we can find D7 brane embeddings with finite baryon density and finite chiral condensation as well as an embedding where only quarks are possible but chiral condensation can be zero or non-zero. We study the phase transition and phase diagram between these phases. We also calculated constituent quark mass and binding energy of baryons as fucntion of the density., Comment: Withdrawn due to the inaccurate title. Replaced by arXive:1203.4883, "Holographic Instanton Liquid and chiral transition."

We compute quantum corrections to finite-size effects for various dyonic giant magnons in the AdS_4 x CP^3 in two different approaches. The off-shell algebraic curve method is used to quantize the classical string configurations in semi-classical way and to compute the corrections to the string energies. These results are compared with the F-term L\"uscher formula based on the S-matrix of the AdS_4 / CFT_3. The fact that the two results match exactly provides another stringent test for the all-loop integrability conjecture and the exact S-matrix based on it., Comment: 21 pages, No figures, corrected typos, added some references