arXiv subjects

A. Tirziu

Publications and source records attributed to A. Tirziu.

At least 19 recordsLinked to original sources

arXiv2010

Exact computation of one-loop correction to energy of pulsating strings in AdS_5 x S^5

In the present paper, which is a sequel to arXiv:1001:4018, we compute the one-loop correction to the energy of pulsating string solutions in AdS_5 x S^5. We show that, as for rigid spinning string elliptic solutions, the fluctuation operators for pulsating solutions can be also put into the single-gap Lame' form. A novel aspect of pulsating solutions is that the one-loop correction to their energy is expressed in terms of the stability angles of the quadratic fluctuation operators. We explicitly study the "short string" limit of the corresponding one-loop energies, demonstrating a certain universality of the form of the energy of "small" semiclassical strings. Our results may help to shed light on the structure of strong-coupling expansion of anomalous dimensions of dual gauge theory operators.

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arXiv2010

Spiky strings in Bethe Ansatz at strong coupling

We study spiky string solutions in AdS3 x S1 that are characterized by two spins S,J as well as winding m in S1 and spike number n. We construct explicitly two-cut solutions by using the SL(2) asymptotic Bethe Ansatz equations at leading order in strong coupling. Unlike the folded spinning string, these solutions have asymmetric distributions of Bethe roots. The solutions match the known spiky string classical results obtained directly from string theory for arbitrary semiclassical parameters, including J=0 and any value of S, namely short and long strings. At large spins and winding number the string touches the boundary, and we find a new scaling limit with the energy given as E-S = n /2/ pi sqrt[1+ 4 pi^2/n^2 (J^2/ln^2 S + m^2/ln^2 S)] ln S. This is a generalization of the known scaling for the folded spinning string.

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arXiv2010

Spiky strings in AdS_3 x S^1 and their AdS-pp-wave limits

We study a class of classical solutions for closed strings moving in AdS_3 x S^1 part of AdS_5 x S^5 with energy E and spin S in AdS_3 and angular momentum J and winding m in S^1. They have rigid shape with n spikes in AdS_3. We find that when J or m are non-zero, the spikes do not end in cusps. We consider in detail a special large n limit in which S ~ n^2, J ~ n, i.e. S >> J >> 1, with (E+S)/ n^2, (E-S)/ n, J/n, m/n staying finite. In that limit the spiky spinning string approaches the boundary of AdS_5. We show that the corresponding solution can be interpreted as describing a periodic-spike string moving in AdS_3 --pp-wave x S^1 background. The resulting expression for the string energy should represent a strong-coupling prediction for anomalous dimension of a class of dual gauge theory states in a particular thermodynamic limit of the SL(2) spin chain.

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arXiv2010

Semiclassical circular strings in AdS_5 and "long" gauge field strength operators

We consider circular strings rotating with equal spins S_1=S_2=S in two orthogonal planes in AdS_5 and suggest that they may be dual to "long" gauge theory operators built out of self-dual components of gauge field strength. As was found in hep-th/0404187, the one-loop anomalous dimensions of the such gauge-theory operators are described by an anti-ferromagnetic XXX_1 spin chain and scale linearly with length L>>1. We find that in the case of rigid rotating string both the classical energy E_0 and the 1-loop string correction E_1 depend linearly on the spin S (within the stability region of the solution). This supports the relation between the rigid rotating string and the gauge-theory operator corresponding to the maximal-spin (ferromagnetic) state of the XXX_1 spin chain. The energy of more general rotating and pulsating strings also happens to scale linearly with both the spin and the oscillation number. Such solutions should be dual to other lower-spin states of the spin chain, with the anti-ferromagnetic ground state presumably corresponding to the string pulsating in two planes with no rotation.

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arXiv2009

Semiclassical rigid strings with two spins in AdS_5

Semiclassical spinning string states in AdS_5 are, in general, characterised by the three SO(2,4) conserved charges: the energy E and the two spins S_1 and S_2. We discuss several examples of explicit classical solutions for rigid closed strings of (bended) circular shape with two non-zero spins. In particular, we identify a solution that should represent a state that has minimal energy for large values of the two equal spins. Similarly to the spiky string in AdS_3, in the large spin limit this string develops long "arcs" that stretch towards the boundary of AdS_5. This allows the string to increase the spin while having the energy growing only logarithmically with S=S_1 +S_2. The large spin asymptotics of such solutions is effectively controlled by their near-boundary parts which, as in the spiky string case, happen to be SO(2,4) equivalent to segments of the straight folded spinning string. As a result, the coefficient of the \log S term in the string energy should be given, up to an overall 3/2 coefficient, by the same universal scaling function (cusp anomaly) as in the folded string case, to all orders in the inverse string tension or strong-coupling expansion.

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arXiv2009

On the dressing phase in the SL(2) Bethe Ansatz

In this paper we study the function chi(x1,x2,g) that determines the dressing phase that appears in the all-loop Bethe Ansatz equations for the SL(2) sector of N=4 super Yang-Mills theory. First, we consider the coefficients c_{r,s}(g) of the expansion of chi(x1,x2,g) in inverse powers of x1, x2. We obtain an expression in terms of a single integral valid for all values of the coupling g. The expression is such that the small and large coupling expansion can be simply computed in agreement with the expected results. This proves the, up to now conjectured, equivalence of both expansions of the phase. The strong coupling expansion is only asymptotic but we find an exact expression for the value of the residue which can be seen to decrease exponentially with g. After that, we consider the function chi(x1,x2,g) itself and, using the same method, expand it for small and large coupling. All small and large coupling coefficients chi^(n)(x1,x2), for even and odd n, are explicitly given in terms of finite sums or, alternatively, in terms of the residues of generating functions at certain poles.

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arXiv2009

Spiky strings in the SL(2) Bethe Ansatz

We study spiky strings in the context of the SL(2) Bethe ansatz equations. We find an asymmetric distribution of Bethe roots along one cut that determines the all loop anomalous dimension at leading and subleading orders in a large S expansion. At leading order in strong coupling (large lambda) we obtain that the energy of such states is given, in terms of the spin S and the number of spikes n by E-S=n sqrt{lambda}/(2 pi) (ln 16 pi S/(n sqrt{lambda})+ ln sin (pi/n) - 1)+ O(ln S/S). This result matches perfectly the same expansion obtained from the known spiky string classical solution. We then discuss a two cut spiky string Bethe root distribution at one-loop in the SL(2) Bethe ansatz. In this case we find a limit where n goes to infinity, keeping (E+S)/n^2, (E-S)/n, J/n fixed. This is the one loop version of a limit previously considered in the context of the string classical solutions in AdS5 x S5. In that case it was related to a string solution in the AdS pp-wave background.

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arXiv2009

Quantum corrections to energy of short spinning string in AdS5

Motivated by desire to shed light on the strong coupling behaviour of anomalous dimensions of "short" gauge theory operators we consider the famous example of folded spinning string in AdS_5 in the limit of small semiclassical spin parameter §= S/sqrt[lambda]. In this limit the string becomes short and is moving in a near-flat central region of AdS_5. Its energy scales with spin as E = sqrt[2 S] [ a_0 + a_1 S + a_2 S^2 + ...]. We explicitly compute the leading 1-loop quantum AdS_5 x S^5 superstring corrections to the short-string limit coefficients a_0 and a_1 and show, in particular, that a_1 receives a contribution containing ζ(3).

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arXiv2009

Structure of large spin expansion of anomalous dimensions at strong coupling

The anomalous dimensions of planar N=4 SYM theory operators like tr(Phi D^S Phi) expanded in large spin S have the asymptotics γ= f ln S + f_c + 1/S (f_11 ln S + f_10) + ..., where f (the universal scaling function or cusp anomaly), f_c and f_mn are given by power series in the `t Hooft coupling λ. The subleading coefficients appear to be related by the so called functional relation and parity invariance (or reciprocity) property of the function expressing γin terms of the conformal spin of the collinear group. Here we study the structure of such large spin expansion at strong coupling via AdS/CFT, i.e. by using the dual description in terms of folded spinning string in AdS_5. The large spin expansion of the classical string energy happens to have the same structure as that of γin the perturbative gauge theory. Moreover, the functional relation and the reciprocity constraints on the coefficients are also satisfied. We compute the leading string 1-loop corrections to the coefficients f_c, f_11, f_10 and verify the functional/reciprocity relations at subleading λ^{-1/2} order. This provides a strong indication that these relations hold not only in weak coupling (gauge-theory) but also in strong coupling (string-theory) perturbative expansions.

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arXiv2008

On the short string limit of the folded spinning string in AdS5 x S5

In this paper we generalize the results of arXiv:0806.4758 to non-zero value J of angular momentum in S^5. We compute the 1-loop correction to the energy of the folded spinning string in AdS_5 x S^5 in the particular limit of slow short string approximation. In this limit the string is moving in a near-flat central region of AdS_5 slowly rotating in both AdS_5 and S^5. The one-loop correction should represent the first subleading correction to strong coupling expansion of the anomalous dimension of short gauge theory operators of the form Tr D^S Z^J in the SL(2) sector.

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arXiv2008

Matching the circular Wilson loop with dual open string solution at 1-loop in strong coupling

We compute the 1-loop correction to the effective action for the string solution in AdS_5 x S^5 dual to the circular Wilson loop. More generically, the method we use can be applied whenever the two dimensional spectral problem factorizes, to regularize and define the fluctuation determinants in terms of solutions of one-dimensional differential equations. A such it can be applied to non-homogeneous solutions both for open and closed strings and to various boundary conditions. In the case of the circular Wilson loop, we obtain, for the 1-loop partition function a result which up to a factor of two matches the expectation from the exact gauge theory computation. The discrepancy can be attributed to an overall constant in the string partition function coming from the normalization of zero modes, which we have not fixed.

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arXiv2008

New open string solutions in AdS_5

We describe new solutions for open string moving in AdS_5 and ending in the boundary, namely dual to Wilson loops in N=4 SYM theory. First we introduce an ansatz for Euclidean curves whose shape contains an arbitrary function. They are BPS and the dual surfaces can be found exactly. After an inversion they become closed Wilson loops whose expectation value is $W=\exp(-\sqrtλ)$. After that we consider several Wilson loops for N=4 SYM in a pp-wave metric and find the dual surfaces in an AdS_5 pp-wave background. Using the fact that the pp-wave is conformally flat, we apply a conformal transformation to obtain novel surfaces describing strings moving in AdS space in Poincare coordinates and dual to Wilson loops for N=4 SYM in flat space.

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arXiv2007

Two-loop world-sheet corrections in AdS_5 x S^5 superstring

We initiate the computation of the 2-loop quantum AdS_5 x S^5 string corrections on the example of a certain string configuration in S^5 related by an analytic continuation to a folded rotating string in AdS_5 in the ``long string'' limit. The 2-loop term in the energy of the latter should represent the subleading strong-coupling correction to the cusp anomalous dimension and thus provide a further check of recent conjectures about the exact structure of the Bethe ansatz underlying the AdS/CFT duality. We use the conformal gauge and several choices of the κ-symmetry gauge. While we are unable to verify the cancellation of 2d UV divergences we compute the bosonic contribution to the effective action and also determine the non-trivial finite part of the fermionic contribution. Both the bosonic and the fermionic contributions to the string energy happen to be proportional to the Catalan's constant. The resulting value for 2-loop superstring prediction for the subleading coefficient a_2 in the scaling function matches the numerical value found in hep-th/0611135 from the BES equation.

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arXiv2007

Strong-coupling expansion of cusp anomaly and gluon amplitudes from quantum open strings in AdS_5 x S^5

An important ``observable'' of planar N=4 SYM theory is the scaling function f(lambda) that appears in the anomalous dimension of large spin twist 2 operators and also in the cusp anomaly of light-like Wilson loops. The non-trivial relation between the anomalous dimension and the Wilson interpretations of f(lambda) is well-understood on the perturbative gauge theory side of the AdS/CFT duality. In the first part of this paper we present the dual string-theory counterpart of this relation, to all orders in lambda^(-1/2) expansion. As a check, we explicitly compute the leading 1-loop string sigma model correction to the cusp Wilson loop, reproducing the same subleading coefficient in f(lambda) as found earlier in the spinning closed string case. The same function f(lambda) appears also in the resummed form of the 4-gluon amplitude as discussed at weak coupling by Bern, Dixon and Smirnov and recently found at the leading order at strong coupling by Alday and Maldacena (AM). Here we attempt to extend this approach to subleading order in lambda^(-1/2) by computing the IR singular part of 1-loop string correction to the corresponding T-dual Wilson loop. We discuss explicitly the 1-cusp case and comment on apparent problems with the dimensional regularization proposal of AM when directly applied order by order in strong coupling (inverse string tension) expansion.

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arXiv2006

Logarithmic corrections to higher twist scaling at strong coupling from AdS/CFT

We compute 1-loop correction E_1 to the energy of folded string in AdS_5 x S^5 (carrying spin S in AdS_5 and momentum J in S^5) using ``long string'' approximation in which S >> J >> 1. According to AdS/CFT E_1 should represent the first subleading correction to strong coupling expansion of anomalous dimension of higher twist SL(2) sector operators of the form Tr D^S Z^J. We show that E_1 smoothly interpolates between the ln S regime (previously found in the J=0 case) and the λ/J^2 ln^3 (S/J) regime (which is the leading correction to the thermodynamic limit on the spin chain side). This supports the universality of the ln S scaling. As in previous work, we also find ``non-analytic'' corrections related to non-trivial 1-loop phase in the corresponding Bethe ansatz S-matrix.

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arXiv2006

Infinite spin limit of semiclassical string states

Motivated by recent works of Hofman and Maldacena and Dorey we consider a special infinite spin limit of semiclassical spinning string states in AdS5 x S5. We discuss examples of known folded and circular 2-spin string solutions and demonstrate explicitly that the 1-loop superstring correction to the classical expression for the energy vanishes in the limit when one of the spins is much larger that the other. We also give a general discussion of this limit at the level of integral equations describing finite gap solutions of the string sigma model and argue that the corresponding asymptotic form of the string and gauge Bethe equations is the same.

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arXiv2006

Asymptotic Bethe Ansatz S-matrix and Landau-Lifshitz type effective 2-d actions

Motivated by the desire to relate Bethe ansatz equations for anomalous dimensions found on the gauge theory side of the AdS/CFT correspondence to superstring theory on AdS_5 x S5 we explore a connection between the asymptotic S-matrix that enters the Bethe ansatz and an effective two-dimensional quantum field theory. The latter generalizes the standard ``non-relativistic'' Landau-Lifshitz (LL) model describing low-energy modes of ferromagnetic Heisenberg spin chain and should be related to a limit of superstring effective action. We find the exact form of the quartic interaction terms in the generalized LL type action whose quantum S-matrix matches the low-energy limit of the asymptotic S-matrix of the spin chain of Beisert, Dippel and Staudacher (BDS). This generalises to all orders in the `t Hooft coupling an earlier computation of Klose and Zarembo of the S-matrix of the standard LL model. We also consider a generalization to the case when the spin chain S-matrix contains an extra ``string'' phase and determine the exact form of the LL 4-vertex corresponding to the low-energy limit of the ansatz of Arutyunov, Frolov and Staudacher (AFS). We explain the relation between the resulting ``non-relativistic'' non-local action and the second-derivative string sigma model. We comment on modifications introduced by strong-coupling corrections to the AFS phase. We mostly discuss the SU(2) sector but also present generalizations to the SL(2) and SU(1|1) sectors, confirming universality of the dressing phase contribution by matching the low-energy limit of the AFS-type spin chain S-matrix with tree-level string-theory S-matrix.

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arXiv2006

Slow-string limit and "antiferromagnetic" state in AdS/CFT

We discuss a slow-moving limit of a rigid circular equal-spin solution on R x S^3. We suggest that the solution with the winding number equal to the total spin approximates the quantum string state dual to the maximal-dimension ``antiferromagnetic'' state of the SU(2) spin chain on the gauge theory side. An expansion of the string action near this solution leads to a weakly coupled system of a sine-Gordon model and a free field. We show that a similar effective Hamiltonian appears in a certain continuum limit from the half-filled Hubbard model that was recently suggested to describe the all-order dilatation operator of the dual gauge theory in the SU(2) sector. We also discuss some other slow-string solutions with one spin component in AdS_5 and one in S^5.

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